The generator matrix

 1  0  1  1  1  1
 0  1  1 2X+2 X+2  2
 0  0  X X+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+97x^4+338x^5+1181x^6+332x^7+94x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=11 and d=16.
This code was found by Heurico 1.16 in 6.87e-008 seconds.