The generator matrix

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

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+204x^36+216x^39+1458x^40+216x^42+72x^45+20x^54

The gray image is a linear code over GF(3) with n=180, k=7 and d=108.
This code was found by Heurico 1.16 in 0.106 seconds.