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.