The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+78x^12+288x^15+486x^16+492x^18+1944x^19+816x^21+1944x^22+468x^24+20x^27+24x^30

The gray image is a linear code over GF(3) with n=30, k=8 and d=12.
This code was found by Heurico 1.16 in 0.024 seconds.