Can a CEL code clear them self or do you have to reset the computer?

I pulled a P0141 and a P1399 code

 

Yes. P0141 is oxygen heater circuit malfunction. Your P1399 code is what is known as a Temporary DTC. It indicates a non specific misfire on cylinders 1-4. If the code went "hard" then it would be P0301-P0304 to take you to the specific cylinder. The PCM/Mil system which throws codes is called OBD Ii on our cars. Not enough room here for specifics on how the system rests itself but if you would like to learn more "Getting to know OBD II" by Birnbaum is an excellent resource. In short if the system goes through a series of warm up cycles (3 to set a hard code from a temp) and 40 to clear a code, without a repeat of the anamaly......the system requests a code clear from the PGM and the Mil light is extinguished.

Utah