The subtitle of Rudd's book promises a higher purpose hidden in your DNA, and the genetic framing runs throughout the Gene Keys, beginning with the name. The claim underneath it needs separating from the metaphor.
The numerical coincidence is real and checkable. The I Ching has sixty-four hexagrams because six lines with two possible states give two to the sixth power, which is sixty-four. The genetic code has sixty-four codons because three bases drawn from an alphabet of four give four cubed, which is also sixty-four. Both are short sequences over small alphabets, and both land on the same total.
The correspondence built on it is not established. Mapping hexagrams to codons has been proposed in various forms since at least the 1970s, well before either Human Design or the Gene Keys, and it has never produced a result in molecular biology. There is no mechanism connecting planetary positions to codon usage, no evidence that contemplating a Gene Key affects gene expression, and no peer-reviewed work testing either proposal.
Rudd inherited the framing from Human Design, which had already described gate activations in genetic terms, and extended it. The codon vocabulary in the Gene Keys is his elaboration of a metaphor already present in the system he came from.
None of this is a reason to omit the claim, which is central to how the system presents itself and should be reported. It is a reason to state it accurately: the arithmetic is a genuine coincidence, the biological mapping is an analogy the system finds meaningful, and the two are different kinds of statement. Practitioners hold the second; only the first can be verified.
Sources Gene Keys: Embracing Your Higher PurposeRichard Rudd with The Human Design SystemRa Uru Hu (Alan Robert Krakower)