The generator matrix

 1  0  0  1  1  1  1  1  0  1  1  0  1
 0  1  0  1  0  1 2X 2X+1  0 2X 2X+1  1  0
 0  0  1  2  2  1 2X+1 2X  1 X+2 2X+2 2X  0
 0  0  0 2X  0  X 2X  X 2X  X  0  0  0
 0  0  0  0  X  X  X  0 2X 2X  0  X  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+70x^18+24x^19+210x^20+246x^21+192x^22+582x^23+594x^24+576x^25+1206x^26+762x^27+606x^28+834x^29+456x^30+60x^31+84x^32+54x^33+4x^36

The gray image is a linear code over GF(3) with n=39, k=8 and d=18.
This code was found by Heurico 1.16 in 0.0522 seconds.