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  1  1  1  1  1  1  X  X  1 X^2  1  1  1  1  1 X^2  1  X  1  0  1  1  X  1  1  X  0  1  1 X^2  1 X^2  1  0  1  0  X  0  1  1  X X^2 X^2  1  1  1  1  1 X^2  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2  0 X^2  X  X X^2+X X^2 X^2+X  X X^2+X X^2 X^2  0  0  0 X^2+X X^2+X X^2+X X^2  0 X^2 X^2  0 X^2+X  X X^2+X X^2  X X^2  0 X^2  0  X  X  0 X^2  0  X  X X^2  0  X  X X^2  X X^2+X  X X^2  X  X  X X^2+X  X X^2 X^2 X^2+X  X  X X^2+X  0  0 X^2  0 X^2 X^2 X^2+X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  0 X^2+X  0 X^2  0 X^2+X X^2  X X^2+X  X  X  X  0 X^2  X X^2 X^2+X X^2  0  X X^2 X^2 X^2+X  X X^2+X  0  0  X X^2+X X^2+X X^2 X^2 X^2+X  X  0 X^2  0  0 X^2 X^2+X  X  0  X  0 X^2+X X^2+X X^2+X  X  X X^2+X X^2+X X^2  0  0  X X^2  X  X X^2
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0 X^2  X  0 X^2+X  X  X X^2+X X^2 X^2+X  0  0  X X^2+X  X  0  0 X^2+X X^2+X  X  0 X^2  X  X  X  0 X^2  X X^2+X  0  X X^2  X X^2+X  0  0  0 X^2+X X^2  X X^2 X^2  X X^2+X X^2  X X^2 X^2+X X^2+X  0  0 X^2  X  0  0  X  X  0 X^2+X  0 X^2+X  X X^2+X  X X^2+X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 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  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 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 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+140x^80+4x^81+294x^82+40x^83+348x^84+144x^85+431x^86+196x^87+442x^88+280x^89+390x^90+196x^91+351x^92+80x^93+243x^94+76x^95+149x^96+4x^97+126x^98+4x^99+76x^100+37x^102+27x^104+14x^106+1x^108+1x^110+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 2.24 seconds.