The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^5+21x^6+20x^7+1x^8+1x^10

The gray image is a code over GF(2) with n=24, k=6 and d=10.
This code was found by Heurico 1.16 in 7.01e-005 seconds.