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

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+21x^80+42x^81+37x^82+46x^83+25x^84+24x^85+19x^86+12x^88+8x^89+4x^90+2x^96+6x^97+3x^98+2x^99+3x^100+1x^102

The gray image is a linear code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.10 in 0.015 seconds.