The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+30x^13+72x^15+168x^16+222x^18+612x^19+324x^21+582x^22+90x^24+66x^25+20x^27

The gray image is a linear code over GF(3) with n=30, k=7 and d=13.
This code was found by Heurico 1.16 in 0.0111 seconds.