The generator matrix

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

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+92x^12+144x^14+336x^15+864x^17+480x^18+2214x^20+608x^21+1152x^23+636x^24+32x^27+2x^30

The gray image is a linear code over GF(3) with n=30, k=8 and d=12.
This code was found by Heurico 1.16 in 0.0212 seconds.