The generator matrix

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

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+66x^18+120x^21+162x^22+144x^24+648x^25+158x^27+648x^28+132x^30+108x^33

The gray image is a linear code over GF(3) with n=39, k=7 and d=18.
This code was found by Heurico 1.16 in 0.00721 seconds.