The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+151x^4+464x^5+720x^6+464x^7+151x^8+48x^9+1x^12

The gray image is a code over GF(2) with n=24, k=11 and d=6.
This code was found by Heurico 1.11 in 0.000313 seconds.