The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+540x^36+216x^37+954x^38+1158x^39+540x^40+1332x^41+1332x^42+216x^43+144x^44+114x^45+12x^48+2x^54

The gray image is a linear code over GF(3) with n=180, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0688 seconds.