The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+60x^30+228x^31+312x^32+282x^33+990x^34+876x^35+2060x^36+2724x^37+3276x^38+3626x^39+2886x^40+1236x^41+452x^42+396x^43+132x^44+70x^45+66x^46+4x^48+4x^51+2x^54

The gray image is a linear code over GF(3) with n=171, k=9 and d=90.
This code was found by Heurico 1.16 in 0.408 seconds.