The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+222x^31+216x^32+530x^33+744x^34+642x^35+1056x^36+1854x^37+942x^38+1862x^39+2790x^40+1368x^41+2048x^42+2298x^43+996x^44+960x^45+810x^46+210x^47+80x^48+30x^49+14x^51+8x^54+2x^57

The gray image is a linear code over GF(3) with n=60, k=9 and d=31.
This code was found by Heurico 1.16 in 1.35 seconds.