The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+222x^15+198x^16+348x^17+1398x^18+1392x^19+2760x^20+7314x^21+7476x^22+11400x^23+20478x^24+19608x^25+21576x^26+28184x^27+19398x^28+14844x^29+13044x^30+4296x^31+1560x^32+1494x^33+120x^34+36x^36

The gray image is a linear code over GF(3) with n=39, k=11 and d=15.
This code was found by Heurico 1.16 in 35 seconds.