The generator matrix

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

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+36x^15+162x^16+1044x^18+648x^19+1944x^20+2016x^21+648x^22+54x^24+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 0.0111 seconds.