The generator matrix

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

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+28x^21+82x^24+90x^27+26x^30+8x^33+8x^36

The gray image is a linear code over GF(3) with n=39, k=5 and d=21.
This code was found by Heurico 1.16 in 0.000705 seconds.