The generator matrix

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

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+42x^27+66x^28+90x^30+102x^31+54x^32+550x^33+246x^34+324x^35+742x^36+348x^37+648x^38+1394x^39+330x^40+432x^41+664x^42+294x^43+88x^45+72x^46+62x^48+10x^51+2x^57

The gray image is a linear code over GF(3) with n=57, k=8 and d=27.
This code was found by Heurico 1.16 in 0.113 seconds.