The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+164x^86+84x^87+210x^88+72x^89+176x^90+48x^91+64x^92+12x^93+57x^94+28x^95+47x^96+8x^97+18x^98+18x^100+4x^101+1x^102+8x^104+3x^108+1x^116

The gray image is a linear code over GF(2) with n=360, k=10 and d=172.
This code was found by Heurico 1.16 in 0.466 seconds.