The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+101x^96+16x^98+6x^100+2x^104+2x^108

The gray image is a code over GF(2) with n=384, k=7 and d=192.
This code was found by Heurico 1.16 in 0.515 seconds.