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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+22x^79+48x^80+42x^81+21x^82+32x^83+28x^84+14x^85+6x^86+6x^87+11x^88+2x^89+1x^90+4x^91+6x^92+2x^93+2x^94+2x^96+4x^97+2x^102

The gray image is a linear code over GF(2) with n=166, k=8 and d=79.
This code was found by Heurico 1.10 in 0 seconds.