The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+312x^28+528x^29+556x^30+1254x^31+1998x^32+1658x^33+3540x^34+4464x^35+3928x^36+6534x^37+7008x^38+5842x^39+6576x^40+5940x^41+2858x^42+3264x^43+1692x^44+448x^45+390x^46+240x^47+10x^48+2x^51+6x^54

The gray image is a linear code over GF(3) with n=57, k=10 and d=28.
This code was found by Heurico 1.16 in 21 seconds.