The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1
 0 X^2  0  0  0  0  0 X^2 X^2  0  0 2X^2 X^2 X^2 X^2 X^2  0 2X^2  0
 0  0 X^2  0  0  0 X^2 2X^2 2X^2  0 2X^2 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0 X^2  0  0 2X^2 2X^2 X^2 X^2  0 X^2  0 X^2  0 2X^2 X^2  0  0
 0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 X^2 2X^2 X^2  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2 X^2 2X^2 2X^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+28x^27+94x^30+108x^33+162x^34+116x^36+648x^37+4374x^38+124x^39+648x^40+96x^42+98x^45+52x^48+12x^51

The gray image is a linear code over GF(3) with n=171, k=8 and d=81.
This code was found by Heurico 1.16 in 0.0661 seconds.