The generator matrix

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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+414x^62+298x^63+828x^65+772x^66+324x^67+3204x^68+1758x^69+2268x^70+5736x^71+1702x^72+324x^73+906x^74+378x^75+432x^77+150x^78+132x^80+42x^81+12x^83+2x^93

The gray image is a linear code over GF(3) with n=315, k=9 and d=186.
This code was found by Heurico 1.16 in 16.8 seconds.