The generator matrix

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

generates a code of length 21 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+138x^31+276x^32+690x^33+942x^34+990x^35+1816x^36+2550x^37+2634x^38+3876x^39+5532x^40+5544x^41+6258x^42+7236x^43+5202x^44+4776x^45+4308x^46+2478x^47+2006x^48+1080x^49+372x^50+248x^51+84x^52+4x^54+4x^57+4x^60

The gray image is a linear code over GF(3) with n=63, k=10 and d=31.
This code was found by Heurico 1.16 in 9.78 seconds.