4 ominoes placed.
 0 1 0 0 2 0
 1 1 1 2 2 2
 0 1 3 0 2 0
 0 3 3 3 4 0
 0 0 3 4 4 4
 0 0 0 0 4 0

4 ominoes placed.
 0 1 0 0 2 0
 1 1 1 2 2 2
 0 1 0 3 2 0
 0 4 3 3 3 0
 4 4 4 3 0 0
 0 4 0 0 0 0

4 ominoes placed.
 0 1 0 0 2 0
 1 1 1 2 2 2
 0 1 0 0 2 0
 0 3 0 0 4 0
 3 3 3 4 4 4
 0 3 0 0 4 0

4 ominoes placed.
 0 1 0 0 0 0
 1 1 1 2 0 0
 0 1 2 2 2 0
 0 3 0 2 4 0
 3 3 3 4 4 4
 0 3 0 0 4 0

3 ominoes placed.
 0 1 0 0 0 0
 1 1 1 2 0 0
 0 1 2 2 2 0
 0 0 0 2 3 0
 0 0 0 3 3 3
 0 0 0 0 3 0

3 ominoes placed.
 0 1 0 0 0 0
 1 1 1 0 0 0
 0 1 2 0 0 0
 0 2 2 2 3 0
 0 0 2 3 3 3
 0 0 0 0 3 0

3 ominoes placed.
 0 0 0 0 1 0
 0 0 2 1 1 1
 0 2 2 2 1 0
 0 3 2 0 0 0
 3 3 3 0 0 0
 0 3 0 0 0 0

3 ominoes placed.
 0 0 0 0 1 0
 0 0 0 1 1 1
 0 0 0 2 1 0
 0 3 2 2 2 0
 3 3 3 2 0 0
 0 3 0 0 0 0

Done.  4 solutions found.