The generator matrix

 1  1  1  1  1  1  1  1  1  X
 0  X  0  0 2X^2 2X^2+X 2X^2+X  X 2X  X
 0  0  X  0 2X^2+X 2X^2+2X X^2+2X  X 2X^2+2X 2X^2
 0  0  0  X 2X^2+2X 2X^2+2X X^2 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 15.

Homogenous weight enumerator: w(x)=1x^0+720x^15+3138x^18+8748x^20+6156x^21+900x^24+20x^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 5.76 seconds.