The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+108x^79+211x^80+274x^81+351x^82+450x^83+599x^84+612x^85+595x^86+654x^87+754x^88+634x^89+564x^90+598x^91+474x^92+418x^93+268x^94+184x^95+146x^96+90x^97+55x^98+30x^99+44x^100+16x^101+13x^102+18x^103+8x^104+2x^105+4x^106+2x^107+2x^108+2x^109+4x^110+4x^111+2x^114+1x^116

The gray image is a linear code over GF(2) with n=352, k=13 and d=158.
This code was found by Heurico 1.16 in 13.9 seconds.