The generator matrix

 1  0  0  1  1  1  1  1  0  1  1  1  1 2X  1  X  0  1  1
 0  1  0  1  0  2  1  2  1  0 2X+1 2X+2 2X  1  2  0  1 2X  0
 0  0  1  2  1  2  1  0  2  2 2X 2X+1 2X+1 X+1  0  1 2X+2 X+1  0
 0  0  0 2X  0  0  0  X  X  0  X 2X 2X  0 2X  X  X  0  X
 0  0  0  0 2X  0 2X 2X  X 2X  X  X 2X 2X  0  X  X  X 2X
 0  0  0  0  0  X  X  X  0 2X  X  0 2X 2X  X  0 2X  0 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+46x^27+36x^28+168x^29+262x^30+228x^31+726x^32+742x^33+732x^34+1896x^35+1708x^36+1362x^37+2856x^38+2224x^39+1338x^40+2352x^41+1246x^42+618x^43+750x^44+268x^45+60x^46+52x^48+10x^51+2x^54

The gray image is a linear code over GF(3) with n=57, k=9 and d=27.
This code was found by Heurico 1.16 in 0.948 seconds.