The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+118x^82+178x^84+162x^86+149x^88+118x^90+96x^92+54x^94+35x^96+28x^98+28x^100+20x^102+11x^104+8x^106+6x^108+4x^110+4x^112+4x^116

The gray image is a linear code over GF(2) with n=178, k=10 and d=82.
This code was found by Heurico 1.10 in 0.094 seconds.