Does this provide the functionality you are looking for? Note that a multi-selectable [`SetterBar`][1] is a [`TogglerBar`][2]. The only problem with the latter is that it cannot be partitioned into a multi-row grid. For your particular problem, I would rather use `Button` instead of `Setter`:

    list = {};
    Dynamic@list
    
    Grid[Table[
       DynamicModule[{pressed = False}, With[{idx = i*6 + j},
         Button[Graphics[{Blue, Disk[]}, ImageSize -> 20], 
          pressed = ! pressed; 
          list = If[pressed, Append[list, idx], DeleteCases[list, idx]], 
          Appearance -> Dynamic@If[pressed, "Pressed", Automatic]]]],
       {i, 0, 1}, {j, 6}]]

![Mathematica graphics](https://i.sstatic.net/kInO1.png)


  [1]: http://reference.wolfram.com/mathematica/ref/SetterBar.html
  [2]: http://reference.wolfram.com/mathematica/ref/TogglerBar.html