The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+4x^6+36x^7+27x^8+376x^9+27x^10+36x^11+4x^12+1x^18

The gray image is a code over GF(2) with n=72, k=9 and d=24.
This code was found by Heurico 1.16 in 3.62e-008 seconds.