If is very much running rich...
Carbs running rich do not need cleaned.
If it is a paper air filter, they must be Replaced, not cleaned.
Clogged air cleaners will not allow enough air to get it, and will cause very rich running.
In other words, it can not breath.
If it is a two stage air cleaner, then I suggest replacing both the foam and the paper.
Do not put any oil on foam 2 stage cleaners.
The oil will clog the paper element.
If it only uses a foam element, then only ever use a very tiny amount of oil then squeeze it all out..
There may be an adjustment on the carb to make it a bit more lean, but do not even try to adjust it wihout a new air cleaner.
Make sure that the plug is gapped wide enough too. We want to make sure that we are getting complete combustion.
New plugs gapped at book spec of .030 and maybe a hair more.
You can test to see if the spark is HOT enough by pulling the plugs and putting the spark plug wire back on the plug. Ground it to a head bolt and crank away.
If you see a repeating bright blue spark across the electrodes., and hear a crisp repeating snapping pop of a spark, then it is plenty hot enough.
Make sure both sides of the twin cylinders perform the same.
Also, make sure there is not a gas smell in the oil.
If so, change the oil. If the carb had a float sticking at one time, gasoline could have leaked into the crankcase.
This would thin the oil.
And it could be seeping past the rings.. fowling the plugs...
Also thinner oil makes for less compression and again incomplete combustion.
You may still need to adjust the main fuel mixture adjustment on the carburetor (if it is adjustable).
If I knew the model number of the engine, and they type number and spec number, I could know for sure.
I checked your carburetor, and it is not adjustable.
You can see parts for your unit here.
I am going to post a carburetor answer below. It is not all for you. Do not try to clean your carburetor again.
It will be good information for some other time.
DO, pay attention to the gasoline storage and quality issues.
Also the selection of what kind of gas to buy (at least 89 octane) and where to buy it.
This may help too.
Your carb is NOT dirty so don't go there again, but do check on the gas.
Also make sure you got exactly the correct spark plugs because the wrong plugs may not be burning hot enough.
Here is my comprehensive carburetor and fuel answer that may give you some ideas.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems. Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
Today's gasoline's contain MTBE and alcohol. (Ethanol) They turn to "Junk and garbage" very quickly. Alcohol is partially water (H2O). And they call it "Oxygenated fuels! It is the oxygen that breaks down the organic compounds in the fuel and turns the gas to "Garbage" (Gum and varnish) The fuels we had just a few years ago had no alcohol in it and would store for longer periods of time before going stale... and fuel stabilizers do almost nothing to prevent the fuel from going bad with the changes in today's fuels.
Do not buy gas from the "Discount" Stations. The discount stations get a reduced price on gas because they may be buying fuel that is nearly 30 days old already. You may be getting fuel that's nearly stale right from the pump when buying from a discount station. Purchase your fuel from the well-known stations such as Shell, BP, Sonoco, Phillips 66 etc.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carburetor.
The carburetor must be removed from the engine. Clean all parts with carburetor cleaner and blow out all the small holes and passageways with compressed air. Remove all of the non-metallic parts since the carburetor cleaner will cause them to be disfigured decompose and plug the carburetor as time goes on.
Wash the carburetor cleaner off of the metal parts by washing them in warm, soapy water then rinsing with clean water. Dry them by blowing it off with compressed air. Make sure that all the passageways are blown dry before reassembling.
Reassemble using a NEW carburetor rebuild kit.
DO NOT TRY TO REASSEMBLE WITHOUT USING A COMPLTE CARBURETOR KIT! You will just end up having to do the job again.
ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carburetor too. Dirt and water from a dirty fuel tank will also plug up the carburetor. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carburetor repair kit.
If you do the work yourself, take pictures or at least make a drawing of where all the linkages, gaskets, and component parts go. Correct reassembly is critical.
If the carburetor still doesn't work correctly, you may have to take it to someone who has an "Ultra-sonic" cleaning machine. This machine uses carb cleaner and ultrasonic vibrations to get the very small passageways clean when traditional methods fail.
If you don't feel comfortable with this kind of repair I would suggest sending it to a reputable shop.
Feel free to contact me here at this question anytime ...even after you hit the "ACCEPT" button ...and I will try to help further.