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  X  X  1  1  1  1  X  X  1  1  1  1  X  X  1  1  1  X  X  1  X  X  X  X X^2  0  1 X^2  1 X^3  1  1  X  X  X  X X^2 X^2  X  X  0 X^2 X^3  1  1  1  1  X  X X^2 X^2 X^3  0  X  X X^2 X^2 X^2  0 X^3  X  X X^2 X^3 X^2 X^3 X^3  1
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^2 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2 X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2 X^2  0 X^3 X^3  0  0 X^3  0  0

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+3x^96+40x^97+4x^98+16x^99

The gray image is a linear code over GF(2) with n=768, k=6 and d=384.
This code was found by Heurico 1.16 in 0.797 seconds.