QS_3 on W (columns = images of w1,w2,w3):
   ['1-1i', '-1+1i', '1-1i']
   ['-1-1i', '2+0i', '-1+1i']
   ['-1+1i', '-1-1i', '1-1i']
rank: 2
kernel: [{2: '1+0i', 0: '0-1i', 1: '1-1i'}]
M * (1, 1+i, i) = ['0+0i', '0+0i', '0+0i']
w3 reduced modulo image: {2: '1+0i'} -> w3 in image? False
(ad_c u1)^2 (u0) = {(1, 1, 0): '1+0i', (1, 0, 1): '1+1i', (0, 1, 1): '0+1i'}
QS_3 of it: 
QS_3((ad u1)^2 u0) = {}
