The generator matrix

 1  1  1  X  1  X
 0  X  0  X X+2 3X+2
 0  0  2  0 2X+2 2X+2
 0  0  0 2X+2 2X 2X+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+119x^4+368x^5+1040x^6+368x^7+119x^8+16x^9+1x^12

The gray image is a code over GF(2) with n=48, k=11 and d=12.
This code was found by Heurico 1.16 in 3.62e-008 seconds.