The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+27x^80+36x^81+28x^82+48x^83+22x^84+12x^85+27x^86+16x^87+11x^88+12x^89+1x^90+1x^92+4x^93+5x^94+1x^96+3x^98+1x^116

The gray image is a linear code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.16 in 0.121 seconds.