The generator matrix

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

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+68x^30+128x^33+90x^36+92x^39+5832x^40+100x^42+96x^45+110x^48+40x^51+2x^54+2x^60

The gray image is a linear code over GF(3) with n=180, k=8 and d=90.
This code was found by Heurico 1.16 in 0.0739 seconds.