The generator matrix

 1  0  1  1  1  1
 0  1 X+1 3X+2  2 3X+2
 0  0 2X  0 2X  0
 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+42x^4+176x^5+588x^6+176x^7+37x^8+4x^10

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.