First off, as far as I can tell I'm not sure you can do a traditional minimax with the way you evaluate the board. Instead of checking to see how many pieces were just turned, you would need to evaluate the entire position, the easiest way just being human pieces minus comp pieces, with maybe bonuses added in for special squares (positive score if human has it, negative score if comp has it). Then your minimax algorithm would look something like this in pseudocode:
Code:
int minimax(int depth, bool max, int &bestX, int &bestY)
{
int dummy;
int bestScore;
if (max==true)
   bestScore=-99999;
else
   bestScore=99999;
int score;
for (int i=0; i<8; i++)
{
   for (int j=0; j<8; j++)
   {
       // make move at i,j, if no move possible, then continue with for loop
       // if depth==maxdepth, evaluate board, erase move, return evaluation
       // else score=minimax(depth+1, !max, dummy, dummy)
       // if this is a max (max==true) then
                // if score>bestScore then bestScore=score, bestI=i, bestJ=j
       // else if this is a min(max==false) then
                // if score<bestScore then bestScore=score, bestI=i, bestJ=j
       // erase move
    }
}
return bestScore;
I think that would work, but you would have to make sure that you have an evaluation function that evaluates the entire board, and also make sure that you are consistent with your evaluations. By that I mean make sure if you make good positions for the comp negative and good positions for the human positive that the minimax starts off looking at min since comp obviously wants the lowest score possible.

But your game is good as it is! This is just an idea if you want to go and try and make the AI stronger.