The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+516x^30+306x^31+672x^32+1738x^33+1302x^34+1626x^35+5402x^36+2592x^37+3006x^38+9762x^39+4134x^40+4554x^41+10210x^42+3522x^43+2712x^44+4400x^45+1206x^46+468x^47+756x^48+60x^49+84x^50+4x^51+16x^54

The gray image is a linear code over GF(3) with n=60, k=10 and d=30.
This code was found by Heurico 1.16 in 85.3 seconds.