The generator matrix

 1  0  0  1  1  1  1  1 2X  1  1  1  X
 0  1  0  0  X 2X+1  2 2X+1  1 X+2  1 2X+2  1
 0  0  1  1 2X+2 2X  0 X+2 2X+1  2  1 X+1 X+2
 0  0  0 2X 2X  0  X 2X 2X  X  X  0  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+260x^21+702x^24+728x^27+494x^30+2x^39

The gray image is a linear code over GF(3) with n=39, k=7 and d=21.
This code was found by Heurico 1.16 in 0.27 seconds.