The generator matrix

 1  1  1  1  1  1  1  1  1  X
 0 X^2  0  0  0 X^2  0 2X^2 2X^2 X^2
 0  0 X^2  0  0 2X^2 X^2  0 2X^2 2X^2
 0  0  0 X^2  0 2X^2 X^2 2X^2  0 X^2
 0  0  0  0 X^2 X^2 X^2 X^2 2X^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+72x^15+222x^18+1458x^20+324x^21+90x^24+20x^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 0.00307 seconds.