The thing we most commonly fail to understand about genetic code is that it is not an isolated abstraction, divorced from context and phenotypical hyper-extension. The genetic code is the component microcosm of the context in which it exists and as the nodal, atomic form of that living world, it bears its experience and history as memory inscribed by the iterative sedimentation of information and complexity upon it.
The genome is the world just as the world in all its diversely radiating uncertainty must in some also sense be the genome writ large. This reflexive relationship is neither contained in or constrained by this particular dichotomous differential. It is, also, the component microcosm as systems symmetry of a relationship and dynamical patterning that is not anchored upon any one instance of its presence, but upon all possible instances at once.
This is precisely why the sum total of all these systems and codes is equivalent to zero. It is subtle and sits just and forever outside the teleological horizons of cognition and language but as presence of conspicuous absence, it remains irreducible, impermeable, unifying. Strange, indeed, but unprovably true.