The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+252x^24+3x^32

The gray image is a code over GF(2) with n=192, k=8 and d=96.
This code was found by Heurico 1.16 in -6.48e-008 seconds.