The generator matrix

 1  1  X  1  1  1
 0  2  2  0  0 2X
 0  0 2X  0 2X 2X
 0  0  0 2X 2X  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+12x^4+32x^5+166x^6+32x^7+11x^8+2x^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 3.62e-008 seconds.