The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+210x^26+326x^27+510x^28+1722x^29+1990x^30+2358x^31+5946x^32+6430x^33+6534x^34+16956x^35+15730x^36+11364x^37+26622x^38+21106x^39+12114x^40+20298x^41+10894x^42+5670x^43+6378x^44+2434x^45+816x^46+600x^47+124x^48+10x^51+4x^54

The gray image is a linear code over GF(3) with n=57, k=11 and d=26.
This code was found by Heurico 1.16 in 73.4 seconds.