The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+16x^1+106x^2+400x^3+975x^4+2656x^5+8076x^6+2656x^7+975x^8+400x^9+106x^10+16x^11+1x^12

The gray image is a code over GF(2) with n=24, k=14 and d=2.
This code was found by Heurico 1.16 in 0.0387 seconds.