The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+50x^24+90x^27+118x^30+486x^32+128x^33+4374x^34+972x^35+118x^36+124x^39+74x^42+16x^45+10x^48

The gray image is a linear code over GF(3) with n=153, k=8 and d=72.
This code was found by Heurico 1.16 in 0.054 seconds.