The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X  0  0  0  0  0  0  X  X  X  0  X
 0  0  X  0  0  0  0  X 2X  X 2X  0  X
 0  0  0  X  0  0  0 2X 2X  0  X 2X  0
 0  0  0  0  X  0  0 2X 2X  X  0  X  0
 0  0  0  0  0  X  0 2X 2X 2X  0  0  X
 0  0  0  0  0  0  X 2X  X  X 2X 2X 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+172x^18+226x^21+1966x^24+3396x^27+412x^30+214x^33+76x^36+10x^39

The gray image is a linear code over GF(3) with n=39, k=8 and d=15.
This code was found by Heurico 1.16 in 0.0455 seconds.