The generator matrix

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

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+62x^24+24x^25+54x^26+78x^27+186x^28+864x^29+1072x^30+636x^31+15066x^32+4036x^33+1110x^34+29268x^35+3988x^36+840x^37+1404x^38+160x^39+120x^40+58x^42+10x^45+10x^48+2x^51

The gray image is a linear code over GF(3) with n=153, k=10 and d=72.
This code was found by Heurico 1.16 in 1.43 seconds.