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Good Morning, I am Kevin.
I think at this point you need to go back to the furnace and check the color coding at the furnace. A couple things I question, most heating systems have a furnace or a heat pump. they usually don't have both. This is very important since the heat pump requires more wires. But then it could have something to do with having 2 wires connected to the R post. You need a wire for W to bring on the heat, this is usually a white wire, but there is no "written code" for this color goes to this terminal. Again, if it is a furnace you can verify this, it will be connected to the W terminal at the furnace.
If you can, take a picture of the wiring you have at the thermostat, and the wiring at the furnace, along with the model numbers of both the indoor and outdoor unit. Use the paper clip to attach and we should be able to get you going.
Have a safe and happy holiday
I think I have your solution for you. To be sure, can you take a picture of the thermostat wires connected to the thermostat please?