The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X 1
0 X 0 0 2X^2 X 2X^2+X X 2X^2 X^2 2X^2+2X 2X 2X^2+X
0 0 X 0 2X^2+X 2X 2X X^2 2X 2X^2 X X^2 2X^2+X
0 0 0 X 2X^2+2X X^2+X X^2+2X 2X^2+X 2X^2 2X X 0 2X^2
generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+84x^19+156x^20+272x^21+516x^22+300x^23+2006x^24+918x^25+9234x^26+3928x^27+1140x^28+420x^29+340x^30+258x^31+96x^32+10x^33+4x^36
The gray image is a linear code over GF(3) with n=117, k=9 and d=57.
This code was found by Heurico 1.16 in 0.23 seconds.