The generator matrix

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

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+88x^15+54x^16+550x^18+540x^19+486x^20+3250x^21+2160x^22+2916x^23+9580x^24+4320x^25+5832x^26+12576x^27+4320x^28+3888x^29+6460x^30+1728x^31+214x^33+76x^36+10x^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 1.79 seconds.