The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+78x^19+156x^20+272x^21+540x^22+300x^23+548x^24+882x^25+486x^26+1012x^27+1164x^28+420x^29+340x^30+252x^31+96x^32+10x^33+4x^36

The gray image is a linear code over GF(3) with n=39, k=8 and d=19.
This code was found by Heurico 1.16 in 0.0587 seconds.