The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+154x^88+336x^89+535x^90+560x^91+627x^92+636x^93+704x^94+596x^95+664x^96+462x^97+507x^98+414x^99+447x^100+350x^101+315x^102+216x^103+209x^104+178x^105+116x^106+64x^107+58x^108+22x^109+11x^110+4x^111+2x^114+2x^115+2x^118

The gray image is a linear code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 5.01 seconds.