All organisms use the same universal code because they (we) are descendants from a common ancestor. Long ago, when life on Earth was first evolving, a primitive organism evolved a primitive, but adequate way of translating its genes into proteins. This system was handed down to its offspring through the generations and all organisms are the descendants of that single ancestor.

From mice to men, from whales to bacteria, the codon AUG will place a methionine in the protein and all the other codons will behave in a similar specific manner across all species because we inherited the translation mechanism from a common ancestor.

Homologous similarities, even those at the biochemical level, are the result of having a common ancestor.

Most of the time we inherit useful things but sometimes useless things are inherited.
A fine example of what I am talking about is a "vestigial organ". Vestigial organs are organs with no apparent use, but which once had a function in the ancestors.

We know that whales and dolphins evolved from land dwelling mammals because of the fossil evidence and the striking amount of homologous similarities in them - from anatomy (as in the arm structures you saw earlier) to their gene sequences. Earlier I mentioned a feature of whales and dolphins that is a vestigial "organ". What trait do whales and dolphins have that is useless to them (but is a link to their mammalian) ancestors?
Give that some thought and then see what I was thinking of.