The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+90x^22+54x^23+120x^24+90x^25+54x^26+78x^27+90x^28+54x^29+42x^30+54x^31+2x^36

The gray image is a linear code over GF(3) with n=39, k=6 and d=22.
This code was found by Heurico 1.16 in 0.00137 seconds.