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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+96x^78+64x^80+34x^82+27x^84+8x^86+14x^88+2x^90+4x^94+4x^96+1x^104+1x^108

The gray image is a linear code over GF(2) with n=162, k=8 and d=78.
This code was found by Heurico 1.10 in 6.22 seconds.