The generator matrix

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

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+165x^80+44x^81+316x^82+116x^83+479x^84+156x^85+368x^86+196x^87+451x^88+196x^89+448x^90+156x^91+396x^92+116x^93+256x^94+44x^95+123x^96+20x^98+28x^100+8x^104+8x^108+3x^112+1x^116+1x^120

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 7.88 seconds.