The generator matrix

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

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+13x^4+82x^5+69x^6+76x^7+10x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.