The generator matrix

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

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+90x^6+240x^9+1260x^12+2520x^15+4620x^18+39366x^20+5040x^21+3870x^24+1700x^27+342x^30

The gray image is a linear code over GF(3) with n=30, k=10 and d=6.
This code was found by Heurico 1.16 in 0.815 seconds.