The generator matrix
1 1 1 1 1 1 X 1 1
0 2 0 0 0 0 2 0 0
0 0 2 0 0 0 2 0 0
0 0 0 2 0 0 2 0 0
0 0 0 0 2 0 2 0 0
0 0 0 0 0 2 2 0 0
generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+15x^4+53x^8+384x^9+32x^10+21x^12+6x^16
The gray image is a code over GF(2) with n=72, k=9 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.