The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+48x^21+756x^22+774x^23+2178x^24+2718x^25+5256x^26+4238x^27+2826x^28+774x^29+96x^30+18x^31

The gray image is a linear code over GF(3) with n=117, k=9 and d=63.
This code was found by Heurico 1.16 in 0.118 seconds.