The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+140x^51+294x^52+198x^53+498x^54+768x^55+564x^56+854x^57+1440x^58+726x^59+1362x^60+2076x^61+1104x^62+1736x^63+2136x^64+1218x^65+1264x^66+1530x^67+462x^68+528x^69+438x^70+102x^71+110x^72+66x^73+40x^75+22x^78+4x^81+2x^84

The gray image is a linear code over GF(3) with n=93, k=9 and d=51.
This code was found by Heurico 1.16 in 2.19 seconds.