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  X  0  X  0  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  1  1  1 X^2  X  X X^2  X
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X X^2+X  0  0 X^2+X  X  0  0  X  X  0  0 X^2+X X^2+X  0  0  X X^2+X  0 X^2+X  0  X X^2 X^2 X^2 X^2 X^2  X X^2  X X^2 X^2+X X^2 X^2+X X^2  X X^2 X^2+X X^2 X^2+X X^2  X X^2  X X^2 X^2+X X^2 X^2 X^2+X  X X^2 X^2  X  X X^2 X^2 X^2+X X^2+X  0  0  X X^2+X  0 X^2+X  0  X  0 X^2+X  0 X^2+X  0  X X^2+X  0  X  X X^2+X  X X^2  0
 0  0  X  X  0 X^2+X X^2+X  0  0 X^2+X  X  0  0  X X^2+X  0 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  X  X X^2  X  X  X  X X^2  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2 X^2+X  X  0  0 X^2+X  X  0  0 X^2+X  X  0  0 X^2+X X^2+X X^2  0 X^2+X  X  0  0 X^2+X  X  0  0  X X^2+X  0 X^2 X^2+X X^2+X  0  0 X^2+X X^2  X  X X^2+X X^2 X^2  0  0
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  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+65x^86+146x^88+123x^90+96x^92+65x^94+10x^96+1x^98+2x^102+2x^104+1x^160

The gray image is a linear code over GF(2) with n=360, k=9 and d=172.
This code was found by Heurico 1.16 in 0.565 seconds.