The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+28x^24+18x^25+54x^26+72x^27+96x^28+324x^29+148x^30+636x^31+1728x^32+416x^33+14064x^34+4968x^35+774x^36+27930x^37+5184x^38+544x^39+876x^40+864x^41+140x^42+120x^43+42x^45+10x^48+10x^51+2x^54

The gray image is a linear code over GF(3) with n=162, k=10 and d=72.
This code was found by Heurico 1.16 in 1.44 seconds.