Step 1: Since each codon is a triplet of 4 possible bases, the total number of codon combinations is $4^3 = 64$.
Step 2: Among these 64, one codon, AUG, is special because it both codes for methionine and marks the start of translation, while 60 other codons code for the remaining amino acids, together making 61 sense codons.
Step 3: The leftover codons, UAA (ochre), UAG (amber) and UGA (opal), do not correspond to any amino acid at all and instead signal the ribosome to stop translation.
Step 4: Counting these gives \[\boxed{3}\]