The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^2+48x^3+135x^4+464x^5+680x^6+464x^7+135x^8+48x^9+36x^10+1x^12

The gray image is a code over GF(2) with n=24, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00115 seconds.