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

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+312x^86+620x^87+975x^88+1184x^89+1650x^90+1628x^91+2265x^92+2108x^93+2376x^94+2264x^95+2584x^96+2184x^97+2422x^98+2112x^99+1900x^100+1480x^101+1528x^102+992x^103+793x^104+540x^105+358x^106+188x^107+157x^108+52x^109+56x^110+4x^111+23x^112+4x^113+2x^114+6x^116

The gray image is a linear code over GF(2) with n=384, k=15 and d=172.
This code was found by Heurico 1.13 in 21.3 seconds.