The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^6+3x^8

The gray image is a code over GF(2) with n=24, k=4 and d=12.
This code was found by Heurico 1.16 in 8.61e-005 seconds.