The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1  0  1  1 X^2  X  1  1  X  1  1 X^2  1  1 X^2+X  1  1  1  1  1  1  X  1  X  X  1  1 X^2  1  X  1  0  1  1  0  1  1  1  1  1 X^2  1 X^2  1  1  X  0  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  0 X^2 X^2 X^2 X^2+X  1  0  1  0  1  1 X^2  X
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  X X+1  1 X^2 X^2+1  1  1 X^2+X  1  1  0 X^2+X+1  1  1 X^2+X  1 X^2+1  0  1 X+1 X+1  X  1 X^2  1  1  X X^2+1  1 X+1  1  X  1 X^2 X+1  1 X^2 X^2+X+1  1 X^2  X  1 X^2  1 X+1 X^2+1  1  1 X^2+X X^2+1  X X^2+1 X^2+1 X^2+X+1  1  1  1  X  1 X^2 X^2  0 X+1  1  1  1  1  1  X  1 X+1  0  1 X^2+X  X X^2
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2 X^2+X  0 X^2 X^2+X X^2 X^2+X  X  0 X^2+X X^2  0  X  0  X X^2  0 X^2+X X^2  0 X^2+X  0 X^2+X X^2+X  X  X X^2  X X^2  X X^2 X^2+X X^2 X^2+X X^2  X X^2  X  0  X  0  0 X^2+X X^2+X  0  0 X^2 X^2  X X^2+X  X X^2+X  0  X  X  X  0  0 X^2+X  X  X X^2 X^2 X^2+X X^2 X^2  X  X X^2  0 X^2  0  X X^2  X X^2+X X^2
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 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  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 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+137x^80+100x^81+259x^82+200x^83+349x^84+232x^85+416x^86+224x^87+343x^88+248x^89+383x^90+264x^91+333x^92+168x^93+169x^94+80x^95+79x^96+20x^97+26x^98+23x^100+19x^102+10x^104+8x^106+2x^108+2x^112+1x^116

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 1.72 seconds.