In Shannon information theory, a code is a mapping between information (bits) and the structures of some medium.
A biological cell stores the instructions for making proteins in DNA. There is a mapping between the information and the structures. Ergo, per Shannon, the mapping between instructions and medium (DNA) is properly referred to as a code. Biologists commonly refer to this as “the genetic code.”
The amount of freedom available for the mapping process is irrelevant to Shannon.
At the same time, Shannon deliberately excludes any inference to meaning or purpose. Thus anyone who would try to infer an intelligent codesmith from the genetic code profoundly misunderstands Shannon information theory.
I believe in a divine codesmith, but that is an act of faith, not an inference from information theory.