The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+251x^92+190x^94+245x^96+150x^98+99x^100+42x^102+32x^104+2x^106+6x^108+2x^120+3x^128+1x^136

The gray image is a linear code over GF(2) with n=384, k=10 and d=184.
This code was found by Heurico 1.16 in 3.09 seconds.