The generator matrix

 1  1  X
 0  X 3X+2
 0  0 2X

generates a code of length 3 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+55x^2+144x^3+55x^4+1x^6

The gray image is a code over GF(2) with n=24, k=8 and d=8.
This code was found by Heurico 1.16 in 6.87e-008 seconds.