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Hi Olga, which truck are we talking about here? model, year, engine, transmission, we need all that info to give an informed answer. And welcome to FTE!.
Ok, you can run those 33" with you current setup, but of course, the acceleration time will be affected a little. The right gearing for that size should be 4.10, and remember you have to match the gearing on both axles or the transfer case (chain driven Borg Warner 1356) will suffer and eventually fail when using the 4WD. You should also consider that size of tire will cause rubbing on several instances, including suspension articulation or flexing, so at least a 2" lift should be installed. That engine is gold and probably has a MAF setup, don't swap any of that (you can still make plenty of performance mods). Your transmission is an E4OD, which would benefit from the mods in the link right down here on my signature.
The codes you posted could be 11 & 35, 11 meaning the system passed one of the self-tests. But I'll let others answer this one.
To summarize your ride:
- Engine: 5.8 or 351 Windsor (351W, not to be confused with the older 351M or newer 5.8 modular engines).
- Transmission: E4OD, an electronically controlled 4 speed auto with overdrive, derived from the older C6.
- Transfer case: Borg Warner 1356.
- Fuel/air management: Most probably MAF (do your air intake tubes join into one before reaching the airbox? that should confirm it).
- ECM: Not so sure, but most probably an OBD II, which means you can retrieve codes with the latest hardware.
You should save that text ^ somewhere for future reference, or use it as a signature in a more compact version, that way others will know what vehicle they're dealing with right away.
Cant really help you on the codes, but with 33/12.50/15 as Encho said you will want 4.10 gears. I am running 33's with stock gears still (3.55) and I could feel a difference, I did lose about 2-3 mpg also.