The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+246x^31+330x^32+148x^33+492x^34+612x^35+186x^36+762x^37+936x^38+194x^39+942x^40+804x^41+156x^42+408x^43+234x^44+38x^45+66x^46+4x^48+2x^51

The gray image is a linear code over GF(3) with n=57, k=8 and d=31.
This code was found by Heurico 1.16 in 4.09 seconds.