The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+45x^70+108x^71+97x^72+140x^73+139x^74+148x^75+161x^76+136x^77+156x^78+92x^79+93x^80+98x^81+86x^82+74x^83+67x^84+78x^85+75x^86+58x^87+30x^88+38x^89+25x^90+22x^91+24x^92+18x^93+14x^94+6x^95+3x^96+4x^97+2x^98+4x^99+4x^100+2x^102

The gray image is a linear code over GF(2) with n=158, k=11 and d=70.
This code was found by Heurico 1.10 in 0.266 seconds.