The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1 X^2+X  1  X X^2+X  1  1 X^2  1  1  X  0  1 X^2  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  X  1  X X^2+X  1  X  1  0  1  0  1  1  1  1 X^2 X^2+X  1  1  X  1  0  1  1 X^2+X  1 X^2+X  1  X  1  1  1  1  1  1  1  0  X  X  1 X^2+X X^2+X X^2+X X^2+X  1 X^2+X  1  X  X  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1 X^2  1  1 X+1 X^2+X  X  1 X^2+X  1  1  1  0  X X^2+X+1 X+1  1 X^2 X^2+X  1 X^2+X X^2+X+1 X^2+X  0  1 X^2  1 X+1 X^2+1  1 X^2  X X+1  1 X^2  X  1 X^2+1 X^2 X^2  1  1  1 X^2+X X^2 X^2+X+1 X^2+X+1  1 X^2 X^2+1 X+1  1  0  1 X^2+X X^2  1  X  1 X^2+X+1  1  1  0 X^2+1 X^2+1 X^2+1 X^2 X^2+X  0  1 X^2+X  X  1  1 X^2+X X^2  1 X^2  X  1 X^2+X  X X^2+X+1 X^2+1 X^2+1 X^2  X  0 X^2  1
 0  0  1 X+1 X^2+X+1  0 X+1  X  1  X  0  1  1  1  X X^2+X X+1 X^2+X  1  1  1 X+1  1  1  0 X^2+X X^2+X+1  X X+1  1  1  X  1 X^2+X+1 X^2  0 X^2+1 X^2+X  1 X^2+X+1  0  1 X^2+X X^2+X  1 X^2 X+1 X^2+X+1  X  X X+1 X^2+X X^2 X^2+1  1 X+1  1  X X^2+X+1 X^2+X X^2+X+1  0  X X^2+1  1 X^2+X+1 X^2+X X^2+1 X^2+1 X+1  0 X^2+X+1  1  1  1 X+1  1 X^2  0  0  1  1 X^2+1  1 X^2+X X^2+X+1  1 X^2  1 X^2 X^2+X  1 X^2+X X^2+1  X  X
 0  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 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  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  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  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 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 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 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  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 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  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+233x^88+284x^89+472x^90+568x^91+583x^92+656x^93+638x^94+708x^95+625x^96+580x^97+452x^98+488x^99+386x^100+388x^101+288x^102+232x^103+181x^104+128x^105+110x^106+48x^107+91x^108+12x^109+16x^110+4x^111+8x^112+6x^114+4x^116+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 11.7 seconds.