The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+68x^27+112x^30+144x^31+240x^33+1152x^34+570x^36+3456x^37+8748x^38+564x^39+3636x^40+396x^42+360x^43+192x^45+24x^48+12x^51+6x^54+2x^57

The gray image is a linear code over GF(3) with n=171, k=9 and d=81.
This code was found by Heurico 1.16 in 0.395 seconds.