The generator matrix

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

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+62x^79+189x^80+306x^81+428x^82+510x^83+561x^84+610x^85+640x^86+664x^87+591x^88+652x^89+620x^90+454x^91+499x^92+452x^93+297x^94+196x^95+165x^96+92x^97+43x^98+48x^99+23x^100+24x^101+15x^102+14x^103+12x^104+6x^105+5x^106+4x^107+4x^108+2x^109+2x^112+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 6.9 seconds.