The generator matrix
1 1 1
0 X 2X+2
generates a code of length 3 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+15x^2+96x^3+15x^4+1x^6
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 3.81e-009 seconds.