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

generates a code of length 96 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=768, k=6 and d=384.
This code was found by Heurico 1.16 in 0.797 seconds.