The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  0  1  1  1  1  1  1 X^2  X  1  1  1  1  1  1 X^2 X^2  1  1  1  X  1  1  X  1  X  1  1 X^2  1 X^2  X  1 X^2  1  1 X^2  1  0  1  X  X  1  1  1  0  0  1  0  0  1  X  1 X^2  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2  0 X^2  X  X X^2+X X^2 X^2+X  X X^2  X  X X^2 X^2  0  X X^2  X  0  X X^2 X^2 X^2+X  0  X  X X^2+X  X  X  0  0 X^2  X  X X^2+X  X  0  0 X^2+X  0  X X^2 X^2+X  0  X  X  0  X X^2+X X^2+X  X  0 X^2+X  0  X  X X^2 X^2+X X^2  0 X^2+X X^2+X X^2  X  0 X^2  X  0  0 X^2 X^2 X^2+X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  X X^2+X X^2  0 X^2 X^2+X  0  X  X X^2+X  0  0  X X^2  0  X  X X^2 X^2+X X^2 X^2 X^2 X^2  X  X  X  X  0 X^2  0 X^2  X X^2+X  0 X^2+X  X  0 X^2 X^2  X  X  X X^2  0 X^2  X  X X^2  X X^2  0 X^2 X^2  X X^2  0 X^2+X  X X^2 X^2+X  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0 X^2  X  0 X^2+X  X  X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2 X^2 X^2+X X^2  0  0  X X^2+X  X  X  0  X  0  X  0  0 X^2+X  0  X X^2  X X^2+X X^2+X X^2 X^2+X X^2+X  0 X^2 X^2+X  0  X X^2+X X^2  0 X^2+X  X X^2  X X^2+X X^2 X^2+X  X  X  X X^2 X^2 X^2+X  X  X X^2+X X^2  X  0  X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 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  0  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 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+37x^86+84x^87+97x^88+176x^89+217x^90+232x^91+268x^92+246x^93+285x^94+334x^95+322x^96+356x^97+296x^98+214x^99+209x^100+146x^101+128x^102+110x^103+84x^104+66x^105+38x^106+32x^107+31x^108+28x^109+18x^110+14x^111+12x^112+2x^113+4x^114+2x^115+4x^117+2x^119+1x^146

The gray image is a linear code over GF(2) with n=384, k=12 and d=172.
This code was found by Heurico 1.16 in 2.55 seconds.