The generator matrix

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

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+60x^13+510x^14+358x^15+4092x^16+3060x^17+23670x^18+15768x^19+61848x^20+47168x^21+15888x^22+4080x^23+482x^24+156x^25+2x^27+4x^30

The gray image is a linear code over GF(3) with n=90, k=11 and d=39.
This code was found by Heurico 1.16 in 4.51 seconds.