The generator matrix

 1  0  0  0  0  1  1  1  1  1  0  X  1  1  1  1  1  1  0  1
 0  1  0  0  0  0 2X  1 2X+1  1  1  1 2X+1 2X+1  X  X X+2 X+2  X  X
 0  0  1  0  0  0 2X+1  1  1 2X  2 X+2  2  X  1 X+1 2X 2X+2  1 2X
 0  0  0  1  0  1 2X+2  X 2X+1  2 2X+2  0 2X+2 2X  1 2X 2X+2 2X+1 X+2  X
 0  0  0  0  1  2 2X+2 2X+2  X  X  2 2X+2  1 2X+1 2X+1  1  2 2X 2X+2 2X
 0  0  0  0  0 2X  X  0 2X  X  X 2X  0  X  0  X 2X  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+54x^27+156x^28+390x^29+1106x^30+1350x^31+1710x^32+3970x^33+4572x^34+5712x^35+11296x^36+10722x^37+14274x^38+22354x^39+17280x^40+17916x^41+21862x^42+12870x^43+10218x^44+9670x^45+4944x^46+2130x^47+1810x^48+594x^49+138x^50+34x^51+12x^54+2x^57

The gray image is a linear code over GF(3) with n=60, k=11 and d=27.
This code was found by Heurico 1.16 in 65.1 seconds.