The generator matrix

 1  1  1  X  X  X
 0 2X  0  0 2X 2X
 0  0 2X 2X 2X  0

generates a code of length 6 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+6x^5+52x^6+3x^8+2x^9

The gray image is a code over GF(2) with n=48, k=6 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.