The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  0  0  0  0  X  X  0  0 2X  X  X  X  X  0 2X  0
 0  0  X  0  0  0  X 2X 2X  0 2X  X  X  X  X  0  0  0  0
 0  0  0  X  0  0 2X 2X  X  X  0  X  0  X  0 2X  X  0  0
 0  0  0  0  X  0 2X  X 2X  X 2X  0  X  X 2X  X 2X  X  0
 0  0  0  0  0  X  X  0  X  X 2X 2X 2X  X  0  X  X 2X 2X

generates a code of length 19 over Z3[X]/(X^2) 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+124x^39+648x^40+96x^42+98x^45+52x^48+12x^51

The gray image is a linear code over GF(3) with n=57, k=7 and d=27.
This code was found by Heurico 1.16 in 0.0227 seconds.