The generator matrix

 1  1  1  1  1  X  1  1  1  1
 0  X 2X  0 2X^2+X 2X^2+X  0  0 X^2 2X
 0  0 X^2  0  0 2X^2  0 X^2 2X^2 2X^2
 0  0  0 X^2  0 2X^2 2X^2 2X^2 X^2  0
 0  0  0  0 2X^2 2X^2 X^2 X^2 X^2 X^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+168x^16+708x^18+612x^19+2916x^20+1296x^21+582x^22+90x^24+66x^25+20x^27

The gray image is a linear code over GF(3) with n=90, k=8 and d=39.
This code was found by Heurico 1.16 in 0.183 seconds.