The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+194x^24+306x^27+270x^28+604x^30+1404x^31+2166x^33+6264x^34+5010x^36+13824x^37+6516x^39+12204x^40+3672x^42+5400x^43+720x^45+330x^48+124x^51+38x^54+2x^57

The gray image is a linear code over GF(3) with n=57, k=10 and d=24.
This code was found by Heurico 1.16 in 7.66 seconds.