The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+249x^70+137x^72+436x^74+160x^76+328x^78+97x^80+248x^82+72x^84+177x^86+19x^88+68x^90+20x^92+22x^94+2x^96+8x^98+4x^100

The gray image is a linear code over GF(2) with n=156, k=11 and d=70.
This code was found by Heurico 1.10 in 119 seconds.