The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+86x^57+36x^58+72x^59+300x^60+96x^61+168x^62+462x^63+222x^64+258x^65+840x^66+456x^67+384x^68+826x^69+336x^70+372x^71+704x^72+264x^73+174x^74+294x^75+48x^76+30x^77+58x^78+40x^81+22x^84+4x^87+8x^90

The gray image is a linear code over GF(3) with n=102, k=8 and d=57.
This code was found by Heurico 1.16 in 0.318 seconds.