The two-side Xominoes are exactly 100 (!). Here is the complete ascii list or the picture of complete set. Don't think that the list is not complete. Remember: "S" becomes "Z" and "Z" becomes "S" if you flip the piece. You can to place the pieces on a square grid.

This is mine. A 10x10 perfect square is not possible.
With 4 sets you could do a 20x20 perfect square.
The one-side Xominoes are 165. Is it possible to do a perfect 11x15 rectangle? I'm optimist.
You could play this puzzle with Windows Paint. It has the rotate 90°, 180°, 270° and mirror functions.
I like the irregular easy solutions as below yet: