The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+172x^68+376x^70+457x^72+472x^74+470x^76+452x^78+419x^80+364x^82+311x^84+222x^86+190x^88+104x^90+53x^92+26x^94+5x^96+2x^100

The gray image is a linear code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.10 in 1.02 seconds.