How can beings of limited intelligence design an intelligence that is superior to their own? If they were capable of doing so, would that not undermine the idea that they have a limit on their intelligence? They must necessarily be intelligent enough to comprehend a state of intelligence greater than their own and imagine it clearly and then bring it into reality.

It would be more apt to say that an intelligence superior to our own would design itself after a certain point, at which point I don't think it's correct to say that we designed it, more that it evolved beyond it's own Human-designed limitations.