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

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+113x^96+10x^100+1x^104+2x^108+1x^120

The gray image is a code over GF(2) with n=768, k=7 and d=384.
This code was found by Heurico 1.16 in 1.06 seconds.