The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+136x^45+12x^47+280x^48+42x^49+90x^50+630x^51+210x^52+474x^53+1626x^54+882x^55+1344x^56+4026x^57+2310x^58+2592x^59+7544x^60+3486x^61+3714x^62+9086x^63+3654x^64+3018x^65+6218x^66+2022x^67+1530x^68+2342x^69+516x^70+348x^71+490x^72+268x^75+116x^78+28x^81+8x^84+6x^87

The gray image is a linear code over GF(3) with n=93, k=10 and d=45.
This code was found by Heurico 1.16 in 18.2 seconds.