There is a bit more flexibility to this than 1:1 mappings, since there are more codons (64) than amino acids coded (20). You could have both CUU and CUC be different characters on the DNA side, that both map to same character on the protein side.
Plausible alternative would be to have the codons or amino acids still code the other half, but have pairs of nucleotides code a 1.5 times longer poem. This would restrict you to 16 different characters, vs. 64 possible codons (minus a few stop codons).
There are around 20-22 amino acids commonly used by known life, so that already restricts you to a bit smaller alphabet than 26 letters.
In this particular case you can consider codons coding for the same amino acid as synonymous, restricting, as you mentioned, the possible mappings to the ~20 proteinogenic amino acids.
Another possibility for expansion would be to take advantage of the genetic code’s degeneracy/redundancy and reprogram it to allow non-canonical amino acids in certain synonymous codons.
Plausible alternative would be to have the codons or amino acids still code the other half, but have pairs of nucleotides code a 1.5 times longer poem. This would restrict you to 16 different characters, vs. 64 possible codons (minus a few stop codons).
There are around 20-22 amino acids commonly used by known life, so that already restricts you to a bit smaller alphabet than 26 letters.