The generator matrix
1 1 1 1 1 1 1 1 1
0 X 2X 0 2X^2+X 2X X^2 2X^2+X X^2+2X
0 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2
generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+54x^15+618x^18+54x^21+2x^27
The gray image is a linear code over GF(3) with n=81, k=6 and d=45.
This code was found by Heurico 1.16 in 0.00056 seconds.