The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+48x^30+36x^31+268x^33+90x^34+216x^35+1098x^36+360x^37+3240x^38+2940x^39+450x^40+6480x^41+3042x^42+396x^43+270x^44+492x^45+126x^46+90x^48+36x^51+2x^54+2x^60

The gray image is a linear code over GF(3) with n=180, k=9 and d=90.
This code was found by Heurico 1.16 in 0.45 seconds.