The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+31x^82+44x^83+61x^84+66x^85+50x^86+54x^87+31x^88+28x^89+24x^90+26x^91+12x^92+10x^93+6x^94+8x^95+13x^96+2x^97+8x^98+6x^99+8x^100+4x^101+3x^102+6x^103+1x^104+2x^105+3x^106+1x^108+2x^110+1x^118

The gray image is a linear code over GF(2) with n=176, k=9 and d=82.
This code was found by Heurico 1.10 in 0.016 seconds.