The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+152x^70+436x^72+674x^74+789x^76+859x^78+844x^80+837x^82+900x^84+807x^86+677x^88+492x^90+333x^92+233x^94+105x^96+37x^98+10x^100+5x^102+1x^104

The gray image is a linear code over GF(2) with n=164, k=13 and d=70.
This code was found by Heurico 1.10 in 4.09 seconds.