The generator matrix

 1  0  1  1  1  1  1 2X^2+X 2X^2  X
 0  1  1  2 2X+1 2X^2  2  1  1  1
 0  0 2X  0  X 2X^2+X X^2+2X 2X^2 2X^2+X X^2+X
 0  0  0 X^2  0 2X^2  0 2X^2 2X^2 2X^2

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+96x^15+612x^16+2808x^18+2052x^19+6318x^20+5436x^21+2160x^22+156x^24+36x^25+8x^27

The gray image is a linear code over GF(3) with n=90, k=9 and d=45.
This code was found by Heurico 1.16 in 0.0877 seconds.