The generator matrix

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

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+48x^82+198x^83+136x^84+358x^85+301x^86+388x^87+260x^88+432x^89+185x^90+342x^91+188x^92+318x^93+173x^94+284x^95+150x^96+144x^97+41x^98+54x^99+18x^100+26x^101+10x^102+12x^104+5x^106+14x^107+2x^108+2x^109+3x^110+1x^112+1x^114+1x^118

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 1.8 seconds.