The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^4+226x^5+517x^6+220x^7+26x^8+2x^9+3x^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 -6.48e-008 seconds.