The generator matrix
1 1 1 1 X X
0 X 0 X+2 0 2
0 0 2 0 2 2
0 0 0 2 2 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+22x^4+84x^6+17x^8+4x^10
The gray image is a code over GF(2) with n=24, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000141 seconds.