The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+160x^3+1111x^4+6368x^5+17488x^6+6368x^7+1111x^8+160x^9+1x^12

The gray image is a code over GF(2) with n=48, k=15 and d=12.
This code was found by Heurico 1.16 in 0.25 seconds.