The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+38x^82+178x^83+177x^84+356x^85+256x^86+414x^87+235x^88+394x^89+220x^90+354x^91+201x^92+358x^93+195x^94+298x^95+129x^96+148x^97+37x^98+24x^99+9x^100+12x^101+7x^102+8x^103+11x^104+10x^105+12x^106+4x^107+4x^108+2x^109+2x^110+1x^122+1x^124

The gray image is a linear code over GF(2) with n=360, k=12 and d=164.
This code was found by Heurico 1.16 in 1.74 seconds.