The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+44x^9+54x^10+190x^12+540x^13+810x^14+708x^15+3618x^16+4860x^17+1796x^18+10152x^19+14094x^20+2308x^21+10152x^22+6480x^23+1290x^24+1728x^25+184x^27+40x^30

The gray image is a linear code over GF(3) with n=30, k=10 and d=9.
This code was found by Heurico 1.16 in 0.636 seconds.