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  X  1  0  1  1  1  1  1  X  1  0  1  1 X^2  1  1  1  1  1  1  X  1  0  1  1  1  X  X  1  1  0  0  0  1  1  1  1  1  X  1  0  X  1  1  X  0  1  1  X  X  1  X  X
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X X^2+X X^2+X X^2 X^2  0  X  X X^2+X  X  0  X  X  0 X^2+X  X X^2 X^2 X^2 X^2+X X^2+X  0 X^2+X X^2+X X^2  X X^2+X X^2+X X^2+X  0 X^2  X  X X^2 X^2+X X^2  0 X^2  X  0 X^2+X X^2+X  0 X^2+X X^2+X  0  X X^2+X X^2 X^2+X  X X^2+X  X  X  X X^2 X^2+X  X X^2  0  0 X^2+X X^2  X  X X^2+X  X  X  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2  0 X^2 X^2+X X^2+X X^2+X  0  X X^2+X X^2+X  0 X^2+X X^2+X X^2 X^2  0  0 X^2 X^2 X^2+X  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  X X^2  0  X  0  X  0 X^2+X X^2 X^2+X  0 X^2+X X^2+X  X  0  X  0  0 X^2  0 X^2 X^2  X  X  0 X^2+X  0  X  0  X X^2 X^2 X^2  0  0  X X^2 X^2 X^2+X  0  X  0 X^2+X X^2  0  0  0  X
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X  X X^2 X^2  0  0  0 X^2 X^2 X^2+X  X X^2+X  X  X  0  X X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  X  0 X^2 X^2+X  0  X X^2+X  X X^2+X  0  0  X X^2+X X^2+X  X  X X^2 X^2+X  X  X X^2  0  0  0  X X^2+X  X X^2 X^2 X^2+X  0  X  0 X^2+X X^2+X X^2 X^2+X  0 X^2  X  X X^2+X X^2  X X^2  X X^2+X X^2  0 X^2 X^2
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X  X X^2+X X^2+X  0 X^2  X  X X^2  0 X^2 X^2+X X^2+X  0  X  0 X^2  X X^2+X  X X^2+X X^2+X X^2  0 X^2  0  X  0 X^2 X^2  X  0 X^2+X  0 X^2+X  X  X  X  0 X^2+X  X X^2  0  0  X X^2+X X^2+X  X X^2+X X^2+X  0  0 X^2+X X^2+X  0 X^2  X X^2 X^2+X  0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2  X X^2 X^2+X  0 X^2+X X^2+X  X X^2+X
 0  0  0  0  0 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 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 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+129x^80+8x^81+284x^82+44x^83+365x^84+132x^85+400x^86+244x^87+473x^88+224x^89+440x^90+168x^91+324x^92+132x^93+244x^94+52x^95+161x^96+16x^97+90x^98+4x^99+66x^100+40x^102+35x^104+6x^106+13x^108+1x^136

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 2.2 seconds.