The generator matrix

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

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+54x^2+128x^3+607x^4+1664x^5+3284x^6+1664x^7+607x^8+128x^9+54x^10+1x^12

The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0204 seconds.