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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+184x^80+28x^81+218x^82+136x^83+246x^84+248x^85+238x^86+412x^87+230x^88+428x^89+172x^90+380x^91+227x^92+276x^93+130x^94+84x^95+157x^96+40x^97+104x^98+12x^99+63x^100+4x^101+24x^102+34x^104+10x^106+7x^108+1x^112+1x^116+1x^128

The gray image is a linear code over GF(2) with n=356, k=12 and d=160.
This code was found by Heurico 1.16 in 20.8 seconds.