The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+234x^32+204x^33+756x^34+1056x^35+1472x^36+3024x^37+5580x^38+2644x^39+3024x^40+1260x^41+244x^42+132x^44+48x^45+2x^48+2x^51

The gray image is a linear code over GF(3) with n=171, k=9 and d=96.
This code was found by Heurico 1.16 in 0.255 seconds.