The generator matrix

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

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+26x^15+582x^16+390x^17+2442x^18+2082x^19+6672x^20+4860x^21+2190x^22+390x^23+40x^24+6x^25+2x^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 0.0777 seconds.