The generator matrix

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

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+96x^12+594x^14+612x^15+2430x^17+1914x^18+6642x^20+2706x^21+3294x^23+1224x^24+162x^26+2x^27+6x^30

The gray image is a linear code over GF(3) with n=30, k=9 and d=12.
This code was found by Heurico 1.16 in 0.391 seconds.