The generator matrix

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

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+44x^27+18x^28+146x^30+180x^31+960x^33+2178x^34+13050x^36+7272x^37+25896x^39+7272x^40+1242x^42+576x^43+162x^45+36x^48+12x^51+4x^57

The gray image is a linear code over GF(3) with n=171, k=10 and d=81.
This code was found by Heurico 1.16 in 1.68 seconds.