The generator matrix

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

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+336x^28+498x^29+608x^30+1314x^31+1764x^32+1836x^33+3450x^34+4278x^35+3940x^36+6516x^37+7938x^38+5188x^39+6696x^40+5598x^41+3162x^42+2994x^43+1680x^44+550x^45+564x^46+114x^47+16x^48+6x^51+2x^57

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 28.3 seconds.