The generator matrix

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

generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+151x^4+464x^5+2768x^6+464x^7+151x^8+48x^9+1x^12

The gray image is a code over GF(2) with n=48, k=12 and d=12.
This code was found by Heurico 1.16 in 0.016 seconds.