The generator matrix
1 1 X
0 X^2+2 X^2+2
0 0 2
generates a code of length 3 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+23x^2+80x^3+23x^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 1.05e-007 seconds.