The generator matrix

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

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+8x^5+13x^6+8x^7+1x^8+1x^10

The gray image is a code over GF(2) with n=24, k=5 and d=10.
This code was found by Heurico 1.16 in 7.51e-005 seconds.