The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+30x^13+72x^15+654x^16+2166x^18+2556x^19+7290x^20+4212x^21+2526x^22+90x^24+66x^25+20x^27

The gray image is a linear code over GF(3) with n=90, k=9 and d=39.
This code was found by Heurico 1.16 in 0.199 seconds.