The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  0  1 X^2+X  1 X^2  1  X X^2+X  1  1  1  1  1  1  0 X^2 X^2+X  1  1  0  X  1 X^2+X  1 X^2+X  1  1  1  1  1  1 X^2+X  1 X^2  X X^2  1 X^2 X^2+X  0  1  1 X^2+X  1  1  1  1  0  X  1  1 X^2 X^2+X X^2 X^2+X  1  1 X^2  1  1  1  1  1 X^2+X  1  1  1  1 X^2+X  1 X^2+X X^2  1  1  1 X^2+X
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X+1  1 X^2+1  1 X^2  1 X^2+X+1 X^2+X  1 X+1  X X^2+1 X^2+X+1  X X^2+X  1  1  X  X X^2  1  1 X+1 X^2 X^2+X+1  1  1  1  1 X^2 X^2+X  X  X X^2  1  1 X^2  1  X  1  1 X+1 X^2+X+1  1 X^2+X  X X^2+X  X  0  1 X+1 X^2  X X^2+X X^2  1  1  1  1 X^2+1  X X^2  X  1 X^2 X^2 X^2+1 X^2+X+1 X+1  1 X^2 X^2  1  0 X+1 X+1  1
 0  0  1  1 X+1  0  1 X+1  1  X X^2+1 X^2+1 X^2  0  0  X X+1  1 X+1  X X^2+X+1  X X+1  1  0 X^2 X^2+X+1  1  X  X  1 X^2 X^2  1 X+1 X^2+X  0 X+1 X^2+X  1  0 X^2+X+1  1 X^2+X+1  X X+1  1 X^2+X+1  1 X^2+X+1  1 X^2+X+1  0 X^2+X+1  0 X^2 X^2+1 X^2+X+1  1  0 X^2+1 X^2  1  1  1 X+1  0  1 X+1 X^2+1  X X+1  X  X  1 X^2+1  1 X^2+X+1 X^2+X+1 X+1  1  1 X^2+1  0 X^2 X^2+X  1
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X  0  X  0  X X^2  X X^2  0 X^2+X X^2+X  X  X X^2+X X^2+X  0  0  0 X^2+X X^2+X X^2+X  X X^2  X X^2 X^2+X X^2  0 X^2  0  0 X^2  X X^2 X^2+X X^2  X  0  X X^2+X X^2+X X^2  0  X X^2+X  0 X^2  X  X X^2 X^2 X^2+X X^2 X^2+X X^2+X X^2  X X^2+X  0  X  X  0  0 X^2+X  X  X X^2 X^2+X X^2  0 X^2+X  X  X X^2+X X^2  X  X
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 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  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  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  0  0 X^2  0 X^2 X^2 X^2  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+172x^79+244x^80+500x^81+436x^82+824x^83+459x^84+752x^85+543x^86+874x^87+436x^88+760x^89+307x^90+514x^91+285x^92+344x^93+208x^94+228x^95+87x^96+100x^97+34x^98+28x^99+11x^100+8x^101+5x^102+14x^103+12x^104+3x^106+2x^107+1x^108

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 4.92 seconds.