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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+44x^66+88x^67+135x^68+194x^69+229x^70+228x^71+230x^72+214x^73+234x^74+236x^75+226x^76+210x^77+182x^78+208x^79+207x^80+214x^81+170x^82+164x^83+141x^84+144x^85+97x^86+72x^87+66x^88+44x^89+54x^90+24x^91+18x^92+4x^93+12x^94+4x^95+2x^98

The gray image is a linear code over GF(2) with n=154, k=12 and d=66.
This code was found by Heurico 1.10 in 0.985 seconds.