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  X
 0  0  0  0  X  X
 0  0  0  0  0  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+90x^2+192x^3+1551x^4+2880x^5+6956x^6+2880x^7+1551x^8+192x^9+90x^10+1x^12

The gray image is a code over GF(2) with n=24, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0678 seconds.