The generator matrix

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

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+68x^5+117x^6+68x^7+1x^8+1x^10

The gray image is a code over GF(2) with n=48, k=8 and d=20.
This code was found by Heurico 1.16 in -3.24e-008 seconds.