The genetic code has two puzzling anomalies: first, when viewed as 64 sub-cubes of a 4x4x4 cube, the codons for serine (S) are not contiguous; and there are amino acid codons with zero redundancy, which goes counter to the objective of error-correction. To make sense of this, the paper shows that the genetic code must be viewed not only on stereochemical, coevolution, and error-correction considerations, but also on two additional factors of significance to natural systems, that of an information-theoretic dimensionality of the code data, which requires that the optimum natural code, as opposed to an engineered one, be characterized by e-dimensionality, and the principle of maximum entropy. One implication of noninteger dimensionality is self-similarity to different scales, and it is shown that the genetic code does satisfy this property, and it is further shown that the maximum entropy principle operates through the scrambling of the elements in the sense of maximal algorithmic information complexity. These two additional considerations explain several aspects of its organization.