The generator matrix

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

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+85x^80+12x^81+188x^82+156x^83+338x^84+236x^85+330x^86+236x^87+368x^88+244x^89+314x^90+276x^91+380x^92+228x^93+286x^94+100x^95+191x^96+48x^97+34x^98+19x^100+14x^104+5x^108+5x^112+1x^116+1x^124

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 1.7 seconds.