The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+132x^94+96x^95+70x^96+96x^97+96x^98+6x^100+8x^102+4x^106+1x^108+1x^112+1x^124

The gray image is a code over GF(2) with n=384, k=9 and d=188.
This code was found by Heurico 1.13 in 0.39 seconds.