There isn't one square inch of land in New Mexico that isn't regulated by the NM building codes, nada. All building code enforcement in New Mexico out side city or village lines is handled by the state.
Some cities have no code enforcement and rely on the state to do it.
That said, there are many areas in New Mexico where you can build without permits of any kind and be left alone. If you choose to build without a permit be prepared for a long long time to get a permit if some Dudley DoRight inspector finds you and decides to enforce the law. We were talking about building and some guy in the office spoke up and asked what we were building. We said Eship, and he was very interested. We then said we were going into Albuquerque to start the permit process.