The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+78x^57+60x^58+108x^59+126x^60+48x^61+96x^63+48x^66+48x^67+54x^68+54x^69+6x^70+2x^81

The gray image is a linear code over GF(3) with n=93, k=6 and d=57.
This code was found by Heurico 1.16 in 0.00923 seconds.