Patterns of Design
If you own a car, you know that it has an engine, doors and, of course, wheels. There are some engineering solutions to transportation problems that are clearly better than others, and no matter who makes the car, designers eventually arrive at the same solutions because they work best.
The same pattern holds true in creation. If you were designing genetic material that did one thing in one type of creature and a similar thing in a completely different type of creature, you would use the best design for both. That would result in similar genetic material in both creatures that was subtly different enough to do its unique job in each creature. As a result of using the best design solution, rather than chance, two very different creatures would have similar genetic material. And that's what we are finding as we learn more about genetics. For example, we know that a particular gene in a developing mouse embryo influences the development of the back part of its brain. A very similar gene in the fly influences the development of its antenna, which are sensors that are tied into the brain. Another gene that is similar in people, fish and flies, influences the unique development of eyes in those creatures.
Similarities like these argue against the chance development of the genetic code. The same Designer that invented the genetic code also gave us His Word, which He also intelligently designed to bring us the knowledge of salvation in Jesus Christ.