The generator matrix

 1  0  0  1  1  1  1  1  0  1  1  1 2X  1  1  1  1 2X  1  1
 0  1  0  1  0  2  1  2  1  0 2X+1 2X+2  1 2X  1  0  0  1  X  0
 0  0  1  2  1  2  1  0  2  2 2X 2X+1 2X+1 2X+1  1  2  0 X+1  1  0
 0  0  0 2X  0  0  0  0  0  0 2X  X 2X  X 2X 2X  X 2X  0 2X
 0  0  0  0 2X  0  0  0  X  X 2X  X 2X 2X  X  X  0  0  0 2X
 0  0  0  0  0  X  0  X  X  0  X  X  X 2X 2X  X  0  0 2X  0
 0  0  0  0  0  0  X 2X  X  X 2X  0  X 2X  0  0 2X  X  X  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+74x^27+66x^28+54x^29+300x^30+534x^31+414x^32+1076x^33+2214x^34+1548x^35+3190x^36+5664x^37+3492x^38+5838x^39+8472x^40+4446x^41+5972x^42+6750x^43+2664x^44+2722x^45+2424x^46+504x^47+390x^48+120x^49+80x^51+34x^54+6x^57

The gray image is a linear code over GF(3) with n=60, k=10 and d=27.
This code was found by Heurico 1.16 in 7.05 seconds.