That looks like Fizzer simply used a standard colour picker... That means it's impossible for me to guess how much work it would be to change, but adding 24 additional colours might
be possible. If done on the right there's even room for the text "Player colours", potentially hyperlinked to an explanation why
you would want to choose exactly those colours.
I did a bit of copy-paste editing in Paint and came up with this, I even misspelled "colours" to better fit in with the rest of the page. ;)
Would this be a correct, complete solution for the issue?