It is difficult to imagine that as a possibility. The spacing of three mRNA nucleotides is pretty important structurally in the process of translation from mRNA to protein via the ribosome. It is difficult for me to imagine a ribosome that could operate arbitrarily between codons of two and three nucleotides, unless I am misunderstanding your comment.

A translational reading frame consists of non-overlapping codons of three nucleotides. If one nucleotide is skipped, the entire downstream message is thus garbled. So how would the translational machinery operate if each codon arbitrarily consisted of two or three nucleotides?

I see what you are getting at, but I think what the other comments are saying is that for the third nucleotide position of a given codon, it does not matter which nucleotide this is. The amino acid to be used would only depend on the first two nucleotides, while the third nucleotide can be AUCG.

Nah, I misunderstood completely.

I was thinking of how a hypothetical code might, in the abstract have evolved from binary, through ternary up to the (current base-4).

I haven't got enough biochem knowledge to speculate how three nucleotides per amino acid can evolve to have three.

They have done this with a four letter expanded codon. The fitness of the bacteria tanks.