The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+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 -3.24e-008 seconds.