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.