The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+72x^22+420x^24+294x^25+324x^26+776x^27+276x^28+12x^30+6x^31+6x^33

The gray image is a linear code over GF(3) with n=117, k=7 and d=66.
This code was found by Heurico 1.16 in 0.00269 seconds.