The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+36x^15+54x^16+72x^18+216x^19+72x^21+216x^22+54x^24+8x^27

The gray image is a linear code over GF(3) with n=30, k=6 and d=15.
This code was found by Heurico 1.16 in 0.00123 seconds.