The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+204x^24+36x^25+54x^26+410x^27+18x^28+6x^30

The gray image is a linear code over GF(3) with n=117, k=6 and d=72.
This code was found by Heurico 1.16 in 0.000576 seconds.