The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  1  2  0  0  0  0  0  0
 0  0 2X  0  0  0  0  0  X  0
 0  0  0  X  0  0  0  0  X  0
 0  0  0  0  X  0  0  0  X  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+74x^6+308x^9+1232x^12+2696x^15+17318x^18+31268x^21+4142x^24+1840x^27+170x^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 0.461 seconds.