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.