The generator matrix

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

generates a code of length 19 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+54x^24+140x^27+182x^30+264x^33+1786x^36+13122x^38+3320x^39+384x^42+244x^45+116x^48+54x^51+16x^54

The gray image is a linear code over GF(3) with n=171, k=9 and d=72.
This code was found by Heurico 1.16 in 0.44 seconds.