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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+74x^80+102x^82+32x^83+340x^84+80x^85+228x^86+96x^87+373x^88+176x^89+432x^90+256x^91+501x^92+176x^93+300x^94+96x^95+286x^96+80x^97+202x^98+32x^99+153x^100+16x^102+24x^104+25x^108+9x^112+4x^116+1x^120+1x^132

The gray image is a linear code over GF(2) with n=364, k=12 and d=160.
This code was found by Heurico 1.16 in 2.7 seconds.