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

generates a code of length 96 over Z4[X]/(X^2+2) 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.