The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+54x^16+366x^18+216x^19+648x^20+666x^21+216x^22+18x^24+2x^27

The gray image is a linear code over GF(3) with n=90, k=7 and d=48.
This code was found by Heurico 1.16 in 0.00177 seconds.