The question is physically meaningless and instead illustrates a natural language paradox.

Let N be the smallest number not definable using 212 characters including spaces, where the English language and any reference to a physical quantity such as number of particles in the universe is also allowed.

Since this yields a definition of N using 212 characters, we have found a contradiction. Therefore there is no such smallest number. This means that every natural number is definable using 212 character, according to the specification of the question.

Therefore g(212) is not defined.

Even worse, since there are only finitely many sentences with at most 212 characters, the number of numbers definable in the specified way is finite. Therefore the argument contradicts the well-known theorem that there are infinitely many natural numbers.

Thus we have found a contradiction in the logical system consisting of the Peano axioms for the natural numbers and the English language, and haven't even used that using physical quantities is allowed.