The top two or three highlight colors contrast quite a bit with the neutralizing grey midtone, so a possibility is to saturate the midtone and desaturate the highlights:

Or, possibly, desaturate the highlights a bit more and leave the midtone alone (couldn't make an example in time.) I could be wrong, but I'd say it's a step in the right direction at least.
Also, that very bright highlight color was almost useless (I couldn't see it until I zoomed in 4x), so cutting that out will drop you to 10 colors with no noticeable effect. (EDIT: You could also drop the second-to-lowest shadow color, since it's so dark -- or, you could brighten it up a tiny bit more and it would be more worth the extra color.)
EDIT: Perhaps a better color edit:
