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

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+39x^86+82x^87+71x^88+82x^89+60x^90+26x^91+32x^92+36x^93+28x^94+14x^95+14x^96+10x^97+7x^98+6x^99+2x^100+1x^102+1x^130

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 0.429 seconds.