ANYTHING 'designed' implies intelligence; of some kind or another.
No it doesn't. That is the whole problem with ID. We in science know that DNA causes the appearance of design, but there is no need to insert and intelligent designer to explain what we observe.
The argument rests on who or what "designed" DNA, but we also know that DNA is able to change and grow or reduce. For instance, some plants have more DNA material than we do.
This is the whole fallacy of the ID argument. It is based on no evidence whatsoever. Also, creation is not in the theory of evolution, as you know by now, and whether DNA was designed or not is immaterial to evolutionary biology.