The generator matrix

 1  0  0  1  1  1  1  1 X+3
 0  1  0 2X+3  1 2X+4  2 X+2  1
 0  0  1 2X+4  1 2X+2 X+3  2 2X+2

generates a code of length 9 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+648x^14+216x^15+1944x^16+2592x^17+7584x^18+3888x^19+2592x^20+216x^21+2x^27

The gray image is a code over GF(3) with n=81, k=9 and d=42.
This code was found by Heurico 1.16 in 3.87 seconds.