If a 4 nucleotide sequence code for an amino acid instead of 3 then theoretically how many unique amino acids could be coded by such a system?

There are four types of nucleotides (A, T, G, C). Normally the codons are made up of 3 nucleotides. Thus there are 43 = 64 possible codon combinations. If the codons are made up of 4 nucleotides, then there would be 44 = 256 possible codon combinations. If the codons are made up of 2 nucleotides, there would be 42 = 16 possible codon combinations.