The generator matrix
1 0 1 1 1 1 1 1 1
0 1 1 2 2X+1 0 X 2X+1 X
0 0 2X 0 X X 2X 0 X
generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+26x^15+66x^16+26x^18+84x^19+24x^21+12x^22+4x^24
The gray image is a linear code over GF(3) with n=27, k=5 and d=15.
This code was found by Heurico 1.16 in 0.000316 seconds.