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It sounds like you have a misfire causing your sputtering and will cause the computer to store a fault. The easiest way would be to have the code read and that will tell you which cylinder it is and you can proceed to check the plug and wire, but either way you will have to have the code cleared with a scan tool even after fixing it. Here in Florida some autoparts stores do this for free. (Autozone)
Yes it could,
I was not aware of the miles, I would also strongly suggest you check the timing belt, the service interval on that is 60,000 miles. As far as the sputtering there are many other things that can cause this, just for example an injector, the computer, the coil, the timing belt jump a tooth. I based my diagnosis on the description you gave that it was sputtering a little, this is usually indicative of a misfire and what I told you was what I have personally seen at the dealership the majority of the time.But do have the code read because that can save you a little time and like I said you will have to get it cleared out anyway because it won`t go away. And do check or have the timing belt checked, this is a weak spot on this engine I have seen many break and cause engine damage.