Yes, I'm a native.

Not all bodies of law would be called a code. "Code" is, I think, always legislative in nature, and specifically indicates a codified or organized and self-contained body of law. For a good example of the difference, compare the United States Statutes at Large with the U.S. Code. I'm not sure if that distinction carries over into the civil law countries, but I'd think it would (in order to revise or add to the civil code, you'd have to enact various statutes).

There's also the "model code" category in the US, where what you're codifying is typically common law principles distilled from court decisions, subject to some attempt at reform by the people involved in developing the model code.