The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+70x^86+120x^87+178x^88+298x^89+411x^90+478x^91+521x^92+572x^93+574x^94+580x^95+661x^96+662x^97+638x^98+602x^99+485x^100+384x^101+248x^102+228x^103+153x^104+106x^105+77x^106+22x^107+29x^108+16x^109+15x^110+16x^111+14x^112+6x^113+10x^114+2x^115+5x^116+4x^117+3x^118+1x^120+1x^126+1x^134

The gray image is a linear code over GF(2) with n=384, k=13 and d=172.
This code was found by Heurico 1.16 in 6.98 seconds.