The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+216x^31+324x^32+148x^33+756x^34+636x^35+2130x^36+1302x^37+6732x^38+4082x^39+1602x^40+828x^41+156x^42+450x^43+228x^44+38x^45+48x^46+4x^48+2x^51

The gray image is a linear code over GF(3) with n=171, k=9 and d=93.
This code was found by Heurico 1.16 in 36 seconds.