The generator matrix

 1  1  1
 0  X X^2+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+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 -6.48e-008 seconds.