The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+36x^37+60x^38+12x^39+42x^40+36x^41+10x^42+24x^43+2x^45+6x^46+12x^47+2x^51

The gray image is a linear code over GF(3) with n=60, k=5 and d=37.
This code was found by Heurico 1.16 in 0.011 seconds.