The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+52x^77+42x^78+53x^80+40x^81+24x^85+20x^86+8x^88+8x^89+4x^93+2x^94+1x^96+1x^144

The gray image is a linear code over GF(2) with n=162, k=8 and d=77.
This code was found by Heurico 1.16 in 53.8 seconds.