The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  0  X  X  X 2X 2X  0  0
 0  0  X  0  0  0  0  0  X 2X 2X  X 2X  X  X  0  0  X  0
 0  0  0  X  0  0  0  X 2X 2X 2X 2X  0  0  X  0  X  X  0
 0  0  0  0  X  0  0 2X 2X 2X  0  X  X  0  X  X  X 2X  0
 0  0  0  0  0  X  0 2X  X  0 2X 2X  X  0  0  X 2X 2X  0
 0  0  0  0  0  0  X  X  0  X 2X  X  X 2X  0  X 2X  0  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+54x^24+140x^27+182x^30+264x^33+1786x^36+3320x^39+384x^42+244x^45+116x^48+54x^51+16x^54

The gray image is a linear code over GF(3) with n=57, k=8 and d=24.
This code was found by Heurico 1.16 in 0.145 seconds.