The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+96x^21+214x^24+258x^27+154x^30+2x^33+2x^36+2x^39

The gray image is a linear code over GF(3) with n=39, k=6 and d=21.
This code was found by Heurico 1.16 in 0.00209 seconds.