The generator matrix
1 1 1
0 2 0
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+3x^2+56x^3+3x^4+1x^6
The gray image is a code over GF(2) with n=24, k=6 and d=8.
This code was found by Heurico 1.16 in 3.62e-008 seconds.