The generator matrix

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

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+74x^51+156x^52+324x^53+536x^54+696x^55+768x^56+1234x^57+942x^58+1062x^59+1660x^60+1170x^61+1356x^62+1996x^63+1422x^64+1302x^65+1786x^66+1056x^67+810x^68+636x^69+348x^70+192x^71+82x^72+42x^73+18x^74+4x^75+4x^78+4x^81+2x^87

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 2.7 seconds.