The generator matrix

 1  0  1  1  1  1  1  0  1  0  1  1  1  1  1  0  1  0  1  1  1  X  1  1  1 2X  1  X  1  X  1
 0  1  1  2  0  1  2  1 2X+1  1  0  2 X+2 2X+1  0  1  X  1  2  2  0  1 X+2  X 2X+1  1 X+2  1 2X+1  1  0
 0  0 2X  0  0  0  0  0  0  0 2X  X  X 2X 2X  0 2X  X  X 2X  X 2X  X  X  0  0  X 2X  0  0  X
 0  0  0  X  0  0  0  X 2X  X  0 2X  X 2X  0 2X  0  X  0 2X  X  0 2X 2X  0 2X 2X 2X 2X  0  0
 0  0  0  0  X  0  X  X  X  X  X 2X  0  X  0  X 2X 2X  0  0 2X 2X 2X  0  0  0  X  0 2X  0 2X
 0  0  0  0  0 2X 2X  0 2X  X  0 2X  X  X 2X  X 2X  0  X  X 2X  X  X  X  X 2X  X  0  0 2X  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+78x^51+66x^52+90x^53+94x^54+222x^55+312x^56+82x^57+474x^58+582x^59+118x^60+720x^61+798x^62+100x^63+858x^64+822x^65+52x^66+498x^67+282x^68+106x^69+78x^70+30x^71+40x^72+28x^75+22x^78+8x^81

The gray image is a linear code over GF(3) with n=93, k=8 and d=51.
This code was found by Heurico 1.16 in 0.277 seconds.