The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+14x^78+36x^79+42x^80+52x^81+32x^82+20x^83+18x^84+12x^85+4x^86+7x^88+2x^90+2x^91+2x^94+4x^95+4x^96+2x^98+2x^99

The gray image is a linear code over GF(2) with n=164, k=8 and d=78.
This code was found by Heurico 1.10 in 0 seconds.