The generator matrix

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

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+136x^88+340x^89+473x^90+654x^91+586x^92+756x^93+597x^94+616x^95+520x^96+622x^97+525x^98+458x^99+364x^100+386x^101+283x^102+246x^103+186x^104+150x^105+114x^106+66x^107+38x^108+44x^109+8x^110+6x^111+5x^112+4x^113+2x^115+4x^116+2x^117

The gray image is a linear code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.11 in 1.92 seconds.