The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+98x^5+277x^6+92x^7+18x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=9 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.