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 X+2  1  0  1  1  1  0  1  2 X+2  2  1  1  X  X  1  1  1
 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  1  3  1  2  X  1  1 X+2  X X+2  2  2 X+1  1  2  0  2 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+2  1 X+1  2  0 X+3 X+2  1  1  1  2 X+2  1  1 X+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+144x^94+80x^95+104x^96+32x^97+120x^98+16x^99+8x^102+1x^104+4x^108+1x^112+1x^120

The gray image is a code over GF(2) with n=384, k=9 and d=188.
This code was found by Heurico 1.16 in 5.02 seconds.