The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+262x^80+92x^81+418x^82+156x^83+483x^84+176x^85+472x^86+184x^87+449x^88+172x^89+384x^90+156x^91+286x^92+72x^93+160x^94+16x^95+81x^96+26x^98+29x^100+8x^102+4x^104+4x^106+2x^108+2x^112+1x^120

The gray image is a linear code over GF(2) with n=348, k=12 and d=160.
This code was found by Heurico 1.16 in 9.75 seconds.