The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+87x^84+134x^86+99x^88+70x^90+36x^92+20x^94+15x^96+26x^98+10x^100+2x^104+2x^106+3x^108+2x^110+1x^112+2x^114+2x^120

The gray image is a linear code over GF(2) with n=178, k=9 and d=84.
This code was found by Heurico 1.10 in 0.031 seconds.