The generator matrix
1 1 1 1 1 X
0 X 2X 0 3 X+6
0 0 3 3 6 6
generates a code of length 6 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+26x^9+108x^10+348x^12+216x^13+30x^15
The gray image is a code over GF(3) with n=54, k=6 and d=27.
This code was found by Heurico 1.16 in 0.000275 seconds.