The generator matrix

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

generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+26x^6+292x^7+785x^8+1916x^9+748x^10+284x^11+38x^12+4x^13+2x^14

The gray image is a code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.