The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^10+600x^12+2160x^13+4464x^15+15930x^16+17880x^18+46440x^19+27240x^21+46440x^22+8820x^24+6912x^25+20x^27+24x^30

The gray image is a linear code over GF(3) with n=30, k=11 and d=10.
This code was found by Heurico 1.16 in 17.7 seconds.