The generator matrix
1 1 1
0 X 2
0 0 X
generates a code of length 3 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 1.
Homogenous weight enumerator: w(x)=1x^0+18x^1+111x^2+764x^3+111x^4+18x^5+1x^6
The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in -6.48e-008 seconds.