The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+54x^4+148x^6+49x^8+4x^10

The gray image is a code over GF(2) with n=24, k=8 and d=8.
This code was found by Heurico 1.16 in 0.00022 seconds.