The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+1020x^96+3x^128

The gray image is a code over GF(2) with n=768, k=10 and d=384.
This code was found by Heurico 1.16 in 0.89 seconds.