The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1 2X^2+X  0  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  1 2X+2  0  1  1 2X^2+2X+1 2X^2+X 2X^2+2X+1  2  0
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2
 0  0  0 X^2  0  0 2X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2  0 2X^2  0  0 X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 2X^2  0 X^2 X^2  0  0  0 X^2 X^2 2X^2 2X^2 2X^2
 0  0  0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 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+64x^30+24x^31+18x^32+272x^33+456x^34+144x^35+2456x^36+2256x^37+9180x^38+8876x^39+4350x^40+18072x^41+8870x^42+3000x^43+288x^44+482x^45+120x^46+74x^48+38x^51+4x^54+4x^57

The gray image is a linear code over GF(3) with n=180, k=10 and d=90.
This code was found by Heurico 1.16 in 1.97 seconds.