A computer search led to the following 16x16 example with a **7/2** rectangle in the middle (scale everything by 1/12):

     0  -3   3   0   0   0   0   0   0   0   0  -6   6   0   0   0
    -1   1  -3   0   3   3  -3   0   0  -3   0   6   0  -3   0   0
     4   2   0   0 -12   9  -3   0   0   0   9 -12   0  -3   6   0
    -6   0   0   0   6 -12  12  -6   0  12 -12   3   3   2  -2  -6
     6   0   0   0   6   0 -12   6  12 -12   0   3   2  -1  -4  12
    -3   0   0   0  -3   2  -2   0  -6   6  -6  12  -5  -7   0   0
     0   0   0   0   3   4  -4  -6   0 -12  12  -6   0  12   0  -6
     0   0   0   0  -6 -12  12   6  12  12 -12  -6   0   0   0   0
     0   9  -6   0   6   2  -2  -4  -2 -10  10   0   5  -9  -2   0
     3  -3   0   0   0   4  -4  -2  -4   4  -4   6   0   4   2  -6
     0  -6   6   0   0   0 -12   6  12 -12   0  -3  -2   1   4   6
    -6   0   0   0   6 -12  12   2  -8  12 -12   3   3   0   0  -6
     8   0  -6   4 -12   9   3  -5  -1   0   9  -6  -4   4   0   3
     0   0   0  -4   4   0   0   3  -7   0   3   1  -2  -1  -4   3
    -2   0   3  -1   0   3   0  -1   2   0  -6  -1   7   0   0   0
    -3   0   6   1   0  -4   0   1  -1  -3   3   0   0   0   0   0