The generator matrix

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

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+1290x^18+5184x^21+17496x^24+23714x^27+10692x^30+648x^33+24x^36

The gray image is a linear code over GF(3) with n=39, k=10 and d=18.
This code was found by Heurico 1.16 in 87.1 seconds.