The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+66x^27+30x^29+192x^30+288x^32+400x^33+1404x^35+998x^36+3702x^38+1810x^39+4842x^41+1836x^42+2592x^44+938x^45+264x^47+202x^48+84x^51+22x^54+10x^57+2x^60

The gray image is a linear code over GF(3) with n=60, k=9 and d=27.
This code was found by Heurico 1.16 in 1.03 seconds.