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  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  X  1 X^2 X^2 X^2  1  X  X  X  X  1 X^2 X^2 X^2  X  1  1  1  X  X  2  2  2  0  0  0  X X^2  X  X X^2 X^2 X^2 X^2  X  X  X  X  X X^2  2  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  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+50x^97+4x^98+4x^101+2x^105

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 0.656 seconds.