The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  X  1  1  0  1
 0  X  0  0  0  X X^2+X X^2+X  0  0  0  0 X^2+X  X  X X^2+X  0  0  X X^2+X  0  X X^2+X  0 X^2  X  X X^2 X^2+X X^2+X X^2  0 X^2+X X^2  0 X^2+X X^2 X^2  X  X  0 X^2  X  X X^2  X  X  0 X^2  0  X X^2  0 X^2+X X^2+X X^2+X X^2  X X^2  0  X  X X^2+X X^2  0 X^2+X X^2  X  0  X X^2  0 X^2+X  X X^2+X  X X^2+X X^2  0 X^2 X^2  0  0 X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2+X
 0  0  X  0  X  X  X X^2 X^2 X^2  X  X  X  X  0 X^2  0 X^2  X  X  X  0 X^2  X X^2 X^2+X X^2  X X^2+X  0 X^2+X X^2 X^2+X  X  0 X^2+X X^2  X  0  0 X^2+X X^2 X^2 X^2+X X^2 X^2 X^2+X  X X^2 X^2+X  X  0 X^2+X X^2  0 X^2+X  X X^2  0 X^2+X  0  X X^2+X  0 X^2 X^2 X^2+X  X X^2+X X^2+X X^2 X^2 X^2  X  0 X^2+X  0 X^2+X  X  0 X^2+X X^2  0  X  0  X X^2 X^2 X^2+X X^2  0
 0  0  0  X  X  0  X  X  X X^2  X X^2 X^2  X  X X^2  0  X  0  X X^2  X X^2 X^2+X  0  0 X^2 X^2 X^2+X  X  X X^2+X X^2  0 X^2+X  X X^2 X^2+X X^2+X X^2  0  0  X X^2+X X^2+X X^2 X^2 X^2+X X^2  0 X^2+X  X  X X^2+X X^2  0 X^2  X X^2+X X^2+X X^2 X^2 X^2+X X^2  0  0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  0 X^2 X^2+X  0 X^2+X X^2  0 X^2 X^2+X X^2 X^2 X^2+X X^2+X  0 X^2+X  X X^2  X  0
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+100x^86+82x^88+128x^89+104x^90+256x^91+68x^92+128x^93+68x^94+28x^96+48x^98+12x^100+1x^176

The gray image is a linear code over GF(2) with n=364, k=10 and d=172.
This code was found by Heurico 1.16 in 0.913 seconds.