The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+54x^20+36x^21+282x^22+240x^23+726x^24+504x^25+2304x^26+1358x^27+576x^28+288x^29+54x^30+96x^31+30x^32+12x^33

The gray image is a linear code over GF(3) with n=117, k=8 and d=60.
This code was found by Heurico 1.16 in 0.029 seconds.