The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 X 1 1 X 0 1 1 1 1 0 1 1 X 1 1 0 1 1 X 1 0 1 X 1 1 0 X 1 1 0 X 1 X X 1 0 1 1 1 X X X 0 0 1 0 0 1 1
0 1 0 0 1 1 1 0 0 1 X+1 X 1 1 X 0 0 1 1 X+1 1 0 X X+1 X 0 1 X+1 X+1 1 X 0 1 X 0 1 X 1 X+1 X X+1 X+1 1 1 X+1 1 1 0 X 0 1 X+1 1 X+1 1 1 1 X 0 1 1 X+1 1 1 0 X
0 0 1 1 1 0 1 0 1 X+1 0 X 0 X+1 1 X+1 1 X 1 0 X+1 1 X X+1 0 1 X+1 0 0 X+1 0 X X X X X X+1 X+1 0 1 0 X X 0 0 X+1 X+1 1 1 1 1 X+1 X+1 X+1 X+1 X+1 0 1 1 0 X X+1 1 0 X+1 0
0 0 0 X 0 0 0 0 0 X X X X X 0 0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X X X 0 X 0 X 0 X X 0 X X X X 0 X X 0 0 X 0 0 X 0 0 0 X 0 0 0 0 X X X
0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X X 0 X X X X 0 X X X X 0 X 0 X 0 0 0 0 X 0 X X 0 X X X X X 0 X 0 0 0 0 0 0 X 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X X 0 0 0 0 0 X 0 X X X X X 0 X 0 0 X X X X 0 0 X X 0 0 0 X X 0 X X 0 X 0 X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X 0 X 0 0 X X 0 X X X 0 X X X 0 X 0 X 0 0 0 X 0 0 X X X X X 0 0 0 X 0 0 X 0 X 0 X 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X X X X X 0 0 0 X 0 0 X 0 X X 0 X X 0 X X X 0 0 0 0 X 0 X 0 X X X 0 X 0 X 0 0 0 0 0 X 0 0 X X
0 0 0 0 0 0 0 0 X X X X X X 0 X 0 0 0 0 0 X 0 X X X 0 0 0 X X 0 0 0 X 0 X 0 X X X 0 0 X 0 0 X 0 0 X X 0 0 X 0 X X X 0 X X X X X X 0
generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+158x^56+228x^58+550x^60+436x^62+519x^64+464x^66+481x^68+412x^70+372x^72+216x^74+161x^76+32x^78+52x^80+4x^82+7x^84+2x^88+1x^92
The gray image is a linear code over GF(2) with n=132, k=12 and d=56.
This code was found by Heurico 1.16 in 2.87 seconds.