I have made a slightly more in-depth analysis of an evolution with 128 circles, looking at individual mutations. I've identified the mutation that caused the largest improvement in fitness (that is to say, the largest (in absolute and relative terms) decrease in distance between the evolved image and the target image). The mutation occurred in the 36th generation and caused the distance value to decrease by ~42 units, or ~13%. The result of the mutation was to swap gene 10 with gene 115, and the effect of the image can be seen below.
In generation 35, gene 10 encoded a large dark circle towards the bottom of the screen and gene 115 encoded a very transparent circle near the top of the screen. The two circles are shown in the third image above (on a blue background so the transparent, light grey circle is visible), which I made when I tired of playing spot-the-difference. Because gene 10 is one of the earliest genes, it was covered by many other circles, which happened to be lighter. In generation 36, the large dark circle towards the bottom of the screen was now gene 115, so was drawn later, over some of the lighter circles. The result is that the bottom of the screen is darker, and so more similar to the target image. If you look at the previous post, you can see that this circle is basically unchanged at generation 100.
This analysis shows that even the most successful mutation in evolutionary history makes a relatively modest difference to the overall image.
All of the largest (successful) mutations occurred in the first few hundred generations as the large regions of shading were becoming settled. It seems that this single gene analysis is unlikely to be informative, but I now have the tools to compare genomes so I could try comparing genomes from more distance generations.