The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 0 1 1 1 1 1 X 1 X X 1 1 1 1 X X 1 X 1 X 1 X X 1 1 X 0 X 1 X 1 1 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 0 X X+1 X X 1 1 0 X 1 0 1 0 X X+1 1 0 X+1 1 0 X X+1 X 1 1 0 0 X X 1 1 X+1 X+1 X X 0 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 X+1 1 X 0 1 0 0 X 1 X+1 X 0 0 X+1 X 1 1 1 X X 1 0 X+1 0 0 X 1 0 1 1 0 0 0 X 1 1 X+1 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 X+1 X 1 0 X X+1 1 X 0 0 X 1 X+1 1 1 X+1 0 0 X+1 X 1 X X 1 0 0 X 0 X+1 1 1 X X 0 1 1 X X
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 X 0 1 X+1 X 1 1 0 X+1 X+1 X X+1 X+1 X 1 X 1 X 0 X 0 1 1 0 X+1 0 1 X 1 X+1 X+1 X X X+1 X 1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 1 0 1 X 1 1 1 1 X 0 0 0 0 0 X+1 X+1 1 X+1 0 X+1 1 1 0 0 X+1 1 X 1 X 0 X X X X+1 X 0 X+1 X

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+42x^56+126x^57+189x^58+212x^59+231x^60+274x^61+220x^62+230x^63+280x^64+224x^65+248x^66+204x^67+230x^68+240x^69+169x^70+184x^71+147x^72+170x^73+138x^74+112x^75+86x^76+46x^77+55x^78+18x^79+6x^80+8x^81+5x^82+1x^84

The gray image is a linear code over GF(2) with n=132, k=12 and d=56.
This code was found by Heurico 1.10 in 0.829 seconds.