The generator matrix
1 0 0 0 1 1 1 X 1 1 0 1 1 0 X 1 1 1 0 X X 0 1 1 1 X X 1 X 1 1 1 X 0 X 0 0 1 1 X 0 0 1 1 1 1 1 1 1 1 1 1 X 1 X 1 0 1 1 X 0 1 1 0 1 X 1 1 1 0 1 1 X X X X 0 0 0 0 0 1 1 1 1 0 X 0 0
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 0 1 X 0 1 1 X 1 X+1 X 1 0 X 1 X X+1 X 1 1 1 1 1 0 0 X 1 0 X+1 1 X 1 X 0 0 1 X+1 1 1 0 X X 1 0 X X X+1 X X 1 X X 0 1 1 0 X+1 1 1 1 1 0 0 X 1 1 X+1 X+1 1 X+1 1 1 1 0
0 0 1 0 0 1 X+1 1 X+1 1 X 0 0 1 1 X 0 X+1 1 X 1 X X+1 0 1 1 X X+1 1 X 0 X+1 0 1 X+1 1 X X X 1 1 X 0 0 0 X+1 X+1 0 0 X+1 X+1 X+1 0 1 0 1 1 0 1 1 1 1 X 1 X+1 X 1 0 1 X 1 1 X X+1 1 X+1 1 1 0 0 0 0 X X X+1 0 1 X 1
0 0 0 1 1 1 0 1 X X+1 1 1 0 X+1 0 0 X+1 X 0 1 X+1 X 0 0 X+1 1 1 X+1 X X+1 1 X 1 X+1 0 0 X 1 0 X+1 1 X+1 X+1 1 X 1 1 X X+1 1 0 X+1 1 1 1 X+1 X X+1 X X+1 1 1 X+1 1 0 1 1 1 0 X+1 X+1 X+1 X+1 X+1 0 1 X X+1 1 1 1 X 1 X X X+1 X+1 1 1
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X 0 X X 0 0 0 0 X X 0 0 X X 0 X X X X X X X 0 X 0 X 0 X 0 X X 0 0 0 0 X X X 0 0 0 X X X 0 0 0 X 0 0 X 0 X 0 X X X 0 X 0 0 0 X 0
0 0 0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X X X 0 0 0 X X X 0 0 0 0 X 0 0 X X X X X 0 0 X 0 X X 0 X 0 0 X X 0 0 X 0 X 0 X X X X X 0 0 0 X X X X 0 X X X X X X X X 0 X X X X X 0 X 0 X
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+100x^82+177x^84+196x^86+159x^88+105x^90+71x^92+45x^94+61x^96+33x^98+20x^100+17x^102+13x^104+10x^106+7x^108+4x^110+2x^112+1x^116+2x^118
The gray image is a linear code over GF(2) with n=178, k=10 and d=82.
This code was found by Heurico 1.16 in 0.33 seconds.