The generator matrix
1 1 1
0 3 0
0 0 3
generates a code of length 3 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+6x^3+228x^6+8x^9
The gray image is a code over GF(3) with n=27, k=5 and d=9.
This code was found by Heurico 1.16 in 3.79e-005 seconds.