The generator matrix

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

generates a code of length 35 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+144x^57+240x^58+510x^59+1014x^60+1020x^61+1194x^62+2228x^63+1962x^64+2280x^65+3652x^66+3192x^67+3636x^68+5352x^69+4044x^70+4380x^71+5894x^72+3924x^73+3468x^74+3936x^75+2292x^76+1620x^77+1422x^78+660x^79+366x^80+346x^81+162x^82+30x^83+60x^84+12x^86+6x^87+2x^93

The gray image is a linear code over GF(3) with n=105, k=10 and d=57.
This code was found by Heurico 1.16 in 28.5 seconds.