The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  0  1  1 2X  1  1  1  1  0  1  1  X  0  1  1  0  1  1  1  1 2X  1
 0  1  0  0  0  1  1  2 2X+2  1 2X+1  2  1 2X+2  0  1 2X X+1 X+1 2X  1 2X X+1  1  X X+2 2X+2  1  X 2X  0 X+2  0 X+1
 0  0  1  1  2  2  1  0 2X+1 2X+1 2X  2  2 2X+1 X+2 X+1  0 X+2 2X X+2  0  X  1 X+2  1  0 X+2  X  1 X+2 X+1 2X  1  0
 0  0  0 2X  0  0  0  0  0  0 2X 2X  X  X  X  X  X 2X  X  X 2X 2X  0 2X  0  X  0  0  X  X  0  X  X  0
 0  0  0  0  X  0 2X 2X  X  X 2X  0 2X 2X 2X 2X  X 2X 2X 2X  X  0  X  0  X  0  X  X 2X  X 2X  0  0  0
 0  0  0  0  0 2X  X 2X  X  0 2X  0 2X 2X  X  X  X  X 2X  0  0  X 2X 2X 2X 2X 2X  X  X 2X  X  X  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+290x^57+186x^58+258x^59+836x^60+450x^61+504x^62+1400x^63+612x^64+762x^65+2258x^66+960x^67+1182x^68+2778x^69+1152x^70+942x^71+2092x^72+738x^73+588x^74+944x^75+204x^76+126x^77+264x^78+72x^79+12x^80+42x^81+18x^84+10x^87+2x^90

The gray image is a linear code over GF(3) with n=102, k=9 and d=57.
This code was found by Heurico 1.16 in 85.4 seconds.