The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  3 2X X+6  X 2X+6 2X
 0  0  X 2X+6  3 2X+6  X X+6 2X+3

generates a code of length 9 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+216x^15+1752x^18+216x^21+2x^27

The gray image is a code over GF(3) with n=81, k=7 and d=45.
This code was found by Heurico 1.16 in 0.00224 seconds.