That would just make amino acids signifiers, and therefore indexes. Codons would then be the signified. All that would mean is you can make a code of the signifieds. And regardless of whether you consider codons indexes or symbols (codons can’t be symbols by the definition of your link, since they’re not defined by culture, tradition, or convention), indexes can still form a code.
But it’s all completely irrelevant. Gonna deal with the evidence that the genetic code evolved, at some point, instead of this endless cycle of appeals to dictionaries, definitions, and credentials?