The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+196x^79+159x^80+642x^81+259x^82+996x^83+351x^84+918x^85+358x^86+966x^87+295x^88+860x^89+233x^90+662x^91+145x^92+466x^93+125x^94+268x^95+59x^96+104x^97+38x^98+36x^99+12x^100+16x^101+9x^102+10x^103+2x^104+2x^105+2x^106+2x^107

The gray image is a linear code over GF(2) with n=348, k=13 and d=158.
This code was found by Heurico 1.16 in 52.7 seconds.