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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+376x^80+32x^81+160x^83+546x^84+356x^85+424x^87+392x^88+604x^89+272x^91+347x^92+156x^93+40x^95+239x^96+4x^97+104x^100+40x^104+2x^108+1x^140

The gray image is a linear code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 94.1 seconds.