The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1 X^2  1  1  0 X^2+X  1 X^2+X  X  1 X^2+X X^2+X  1  1 X^2  1  1  1  1  1  0  X  0  1  1  0  1 X^2+X X^2+X  1 X^2+X  1  0 X^2  1 X^2 X^2+X  1  1 X^2 X^2+X  1  X  1  0  X  0 X^2  1 X^2+X  1  1  1  X  1  X X^2  1 X^2+X  1  X  1  1  1  1  1 X^2  0  1  X  1  0  1 X^2  1 X^2+X  1  1  1  X  0  1  0  1  0
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1  1 X^2 X+1  1  1 X^2+X  X  1 X^2+X X^2+X+1 X^2 X^2+1 X^2 X^2 X^2+X+1 X+1  1  1  1 X^2+1  X  X  1  1 X^2+X  0  1 X^2+X  1  1 X^2  1  1 X^2+X+1  X  1  1  1 X^2 X+1 X^2 X^2  X  1  1  X X^2+X+1 X^2+X  0  X X^2+1  1 X^2+X X^2+X+1 X^2+X  X X^2 X^2+X+1 X+1 X^2+X+1  1  0 X^2 X^2 X^2+X  1 X^2  1  0  1  1  1  0 X^2+X X^2+X+1 X^2+X X^2  0  X X^2  1
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X+1 X^2 X^2  1 X+1  1  X  1 X^2+X  X X^2+X+1  0  1  0  0 X^2 X^2+X X^2+1 X^2+X X^2+X X+1 X^2 X+1  1  1 X+1 X^2  1  1 X^2+1  X X^2+X  0  1  1  0 X^2+1 X^2+1  1 X+1  1  0  X  1  X  0  X  1  0 X+1  X X^2+X X+1 X^2+1  1  1 X^2  0 X^2+X X^2+1 X^2+X  1 X^2+X+1  1  1  1  1 X+1  X X^2+X+1  X X^2+X+1  0 X^2  0 X^2+X+1 X^2+1 X^2  1 X^2+X+1  1 X+1 X^2
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2  0 X^2+X+1 X^2+1  1 X+1 X^2+1  1 X^2+1  1 X^2 X^2+X X^2+X  X X^2+1 X^2 X+1 X^2+1 X^2+X  X X^2+X+1  1  X X^2+X X^2 X^2+X+1  0  0 X+1  X X+1 X^2+X  0 X^2+X X^2+X X+1  0  X X^2+X+1  0 X^2 X+1  1  X X^2+X  1 X^2 X^2+X X^2+X+1  1 X^2+1  0  X X^2+X X^2+X+1 X^2+X+1  1  1 X^2  X X^2+X X^2 X^2+X+1 X^2  0  X X^2+1  0 X^2+X X^2+1 X^2+X+1 X^2+X+1 X^2 X+1 X^2+X  X X^2+X+1  X  1 X^2+X+1 X^2+X  1 X^2+X  X
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X+1  X X^2 X^2+X+1  X  X X^2+X+1 X^2 X+1 X^2+X+1 X+1  0 X^2+X X^2+X+1 X^2+X+1 X+1 X^2  X X^2+X+1 X^2 X^2+X X^2+1 X^2+1 X^2+X X^2+1  X X^2  1 X^2+X+1  1 X^2 X^2+X+1 X^2+1 X^2+1 X^2+1  X X^2+X X^2+1 X^2+X+1 X+1 X^2+X+1 X^2+1 X+1  1 X^2 X+1  X X+1 X^2+1 X^2  1 X^2+1  1 X+1 X^2+1 X^2+X+1 X^2+X X^2+X  0  1  1  X  1  0  X  1 X^2+X  0 X^2 X+1  1 X^2+X X^2+1  1  X X^2+X+1 X^2+X+1 X^2+X  1 X^2+1 X^2+X+1 X^2+X+1  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+264x^86+668x^87+965x^88+1226x^89+1578x^90+1706x^91+2181x^92+2154x^93+2377x^94+2408x^95+2417x^96+2220x^97+2508x^98+1994x^99+1857x^100+1616x^101+1331x^102+1020x^103+871x^104+588x^105+346x^106+170x^107+148x^108+74x^109+38x^110+16x^111+8x^112+10x^113+6x^114+2x^115

The gray image is a linear code over GF(2) with n=384, k=15 and d=172.
This code was found by Heurico 1.16 in 67.3 seconds.