The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1
 0  1  1  2  0  1  2  1  0 2X+1  2  0 2X+1
 0  0 2X  0  0  0  0  0  X 2X 2X  X 2X
 0  0  0  X  0  0  0  X 2X 2X  X  0  X
 0  0  0  0  X  0  0 2X 2X  0 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X  X 2X  X  X
 0  0  0  0  0  0  X  X  X  X  0 2X  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+88x^15+280x^18+162x^20+1090x^21+486x^22+972x^23+3100x^24+1944x^25+1944x^26+3936x^27+1944x^28+1296x^29+2140x^30+214x^33+76x^36+10x^39

The gray image is a linear code over GF(3) with n=39, k=9 and d=15.
This code was found by Heurico 1.16 in 0.243 seconds.