The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+12x^24+54x^26+8x^27+4x^30+2x^39

The gray image is a linear code over GF(3) with n=39, k=4 and d=24.
This code was found by Heurico 1.16 in 0.000375 seconds.