The generator matrix

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

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+24x^15+66x^16+228x^17+294x^18+660x^19+1020x^20+1770x^21+3774x^22+2820x^23+5766x^24+9816x^25+4524x^26+8300x^27+9816x^28+3516x^29+3354x^30+2112x^31+1014x^32+150x^33+18x^36+6x^39

The gray image is a linear code over GF(3) with n=39, k=10 and d=15.
This code was found by Heurico 1.16 in 2.42 seconds.