Are codons in RNA layered? Are we misinterpreting RNA codons?
This relates to the concept of the reading frame, which is the point at which you start dividing 3-letter sequences into codons. As you point out, there are multiple ways to divide a string of amino acids into triplets - in fact, there are six unique ways, found by shifting the start letter by one three times, and doing the same but reading in reverse.
Typically, there is one commonly used frame which can be transcribed and turned into protein, called the open reading frame. But it is not unheard of for a single piece of DNA to encode multiple, overlapping genes, depending on where you start reading it. So, the sequence you show cannot encode 13 amino acids in a single string, but it can encode three different strings, one of which has 5 amino acids and the other two which have 4 amino acids each.
See Multiple Reading Frames at Wikipedia, which shows the following example of a single piece of human DNA which encodes two different genes, MT-ATP6 and MT-ATP8.