The generator matrix

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

generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+3x^16

The gray image is a code over GF(2) with n=96, k=6 and d=48.
This code was found by Heurico 1.16 in -3.24e-008 seconds.