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.