The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^3+151x^4+752x^5+2256x^6+752x^7+151x^8+16x^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 1.05e-007 seconds.