Genetic algorithm does not always find the global optima and a higher mutation rate finds a better solution
I'll start with the second question because it's easier.  How could increasing the mutation rate improve the results?

Genetic algorithms can beat random searches when they converge on the right answer.  Similar to other machine learning algorithms, genetic algorithms have an "explore" phase and a "converge" phase.  If the algorithm doesn't run long enough (enough rounds) to enter the converge phase, then a higher mutation rate will likely give you better results.  The other culprit may be that the utility score of offspring may be independent of the utility score of the parents even though their parameters are very similar.  If this is the case (especially around "good" results) then convergence may be impossible and random search would outperform genetic algorithms.

The other question "Why didn't I ever find the best solution?" could also have a few explanations.  First, you could have just been unlucky - especially if you didn't run your experiment very many times.  Intuitively, a single run searching 10% of the space will have roughly a 10% chance of finding the best solution.  Second, it may be that all antenna configurations which are similar to an optimal solution have low scores.  This would make it less likely to produce the optimal solution genetically.