The generator matrix

 1  1  1  X  1  1
 0 2X+2 2X 2X+2  2  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+8x^5+45x^6+8x^7+1x^8+1x^10

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 0 seconds.