The generator matrix

 1  1  1  1  1  1  X  1  1  1
 0  X  0 2X^2+X 2X X^2 2X^2+X X^2 X^2+X X^2
 0  0  X 2X^2+2X X^2 2X^2+2X X^2+2X 2X X^2+2X 2X^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+22x^15+36x^16+42x^17+302x^18+60x^19+1050x^20+516x^21+42x^22+42x^23+44x^24+24x^25+6x^27

The gray image is a linear code over GF(3) with n=90, k=7 and d=45.
This code was found by Heurico 1.16 in 0.00272 seconds.