The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+338x^18+1950x^21+5772x^24+7618x^27+3900x^30+78x^33+26x^36

The gray image is a linear code over GF(3) with n=39, k=9 and d=18.
This code was found by Heurico 1.16 in 38 seconds.