The generator matrix

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

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+30x^3+146x^4+642x^5+2460x^6+642x^7+141x^8+30x^9+4x^10

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 -6.48e-008 seconds.