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  1  1  1  0  1  1  X  1  1  1  1  1  X  1  X  1 X^2  1  1  1  1  X  1  1  1  1  X  0  1  1  0  X  1 X^2  1  1  1  X  0  1  1  X X^2  1 X^2 X^2  1  1  X  1  1 X^2  1  X  1  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2  0 X^2  X  X X^2+X X^2 X^2+X  X X^2+X X^2 X^2  X  0  X  X  X X^2 X^2  0  X  0  0 X^2 X^2  X  X  X  X X^2+X  X X^2 X^2 X^2  0  X  X X^2+X  0  0 X^2+X  X  X X^2  0  X X^2+X  0 X^2  0 X^2+X  X  0  X  X X^2  X X^2 X^2+X X^2+X  0 X^2+X  X  0  0  0  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  0 X^2+X  0 X^2  0 X^2+X X^2+X X^2+X X^2  X  0  0 X^2 X^2 X^2  0  X X^2+X X^2 X^2 X^2+X  X X^2 X^2+X  X  X  X  0 X^2+X  0  X  X  0 X^2+X  0  X  0  X  0  0  X  X X^2  0 X^2+X X^2  X  X X^2+X X^2 X^2+X X^2  X  X X^2  0  X  0  0 X^2+X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0 X^2  X  0 X^2+X  X  X X^2+X X^2 X^2+X  0  0  X  X  0  X X^2+X X^2 X^2+X  0 X^2+X  X  X X^2 X^2+X X^2+X  X  X X^2+X X^2 X^2 X^2  0  0 X^2+X X^2 X^2 X^2  0  X  X X^2  0  0  0  0  0 X^2+X  0 X^2 X^2 X^2 X^2+X  X X^2  X  0  X X^2  X  0  0 X^2 X^2+X X^2+X X^2 X^2+X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 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 80.

Homogenous weight enumerator: w(x)=1x^0+23x^80+78x^81+112x^82+132x^83+229x^84+136x^85+407x^86+124x^87+533x^88+80x^89+575x^90+96x^91+534x^92+94x^93+321x^94+86x^95+139x^96+66x^97+91x^98+56x^99+48x^100+40x^101+18x^102+12x^103+20x^104+16x^105+9x^106+4x^107+9x^108+2x^109+2x^110+2x^111+1x^138

The gray image is a linear code over GF(2) with n=360, k=12 and d=160.
This code was found by Heurico 1.16 in 2.26 seconds.