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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+53x^68+72x^69+154x^70+180x^71+257x^72+228x^73+198x^74+260x^75+227x^76+230x^77+168x^78+222x^79+218x^80+220x^81+194x^82+200x^83+160x^84+136x^85+144x^86+116x^87+108x^88+116x^89+83x^90+44x^91+50x^92+18x^93+17x^94+2x^95+12x^96+4x^97+1x^98+2x^100+1x^102

The gray image is a linear code over GF(2) with n=158, k=12 and d=68.
This code was found by Heurico 1.10 in 1.03 seconds.