The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  X  0
 0  0  X  0  0  0  0  0 2X  0
 0  0  0  X  0  0  0  0 2X  0
 0  0  0  0  X  0  0  0 2X  0
 0  0  0  0  0  X  0  0 2X  0
 0  0  0  0  0  0  X  0 2X  0
 0  0  0  0  0  0  0  X  X  0

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+56x^6+128x^9+476x^12+896x^15+1316x^18+13122x^20+1568x^21+1262x^24+688x^27+170x^30

The gray image is a linear code over GF(3) with n=30, k=9 and d=6.
This code was found by Heurico 1.16 in 0.0906 seconds.