The generator matrix

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

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+116x^30+138x^31+366x^32+602x^33+3072x^34+1200x^35+6224x^36+11280x^37+9756x^38+11658x^39+11472x^40+1668x^41+960x^42+222x^43+132x^44+102x^45+60x^46+16x^48+4x^51

The gray image is a linear code over GF(3) with n=171, k=10 and d=90.
This code was found by Heurico 1.16 in 1.95 seconds.