The generator matrix

 1  0  0  1  1  1  1  1  0  0
 0  1  0  1  0  2  1  2  1  1
 0  0  1  2  1  2  1  0  2  0
 0  0  0 2X  0  0  0  X  X  X
 0  0  0  0 2X  0 2X 2X  X  X
 0  0  0  0  0  X  X  X  0  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+132x^12+432x^14+720x^15+2592x^17+1788x^18+6642x^20+2544x^21+3456x^23+1332x^24+20x^27+24x^30

The gray image is a linear code over GF(3) with n=30, k=9 and d=12.
This code was found by Heurico 1.16 in 0.176 seconds.