The generator matrix

 1  1  1  1  1  1  1  1  X  X
 0  X  0 2X^2+X X^2  X 2X 2X 2X^2 X^2
 0  0  X X^2+2X 2X^2+2X  X  0 X^2 2X^2+X  X
 0  0  0 X^2  0 2X^2 2X^2 X^2 X^2 X^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+396x^16+216x^18+1188x^19+2916x^20+252x^21+1296x^22+156x^24+36x^25+8x^27

The gray image is a linear code over GF(3) with n=90, k=8 and d=45.
This code was found by Heurico 1.16 in 0.0179 seconds.