The generator matrix

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

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+442x^30+870x^33+5496x^36+10080x^39+1080x^42+720x^45+330x^48+124x^51+38x^54+2x^57

The gray image is a linear code over GF(3) with n=57, k=9 and d=24.
This code was found by Heurico 1.16 in 4.11 seconds.