The generator matrix

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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+102x^61+282x^62+536x^63+894x^64+1722x^65+3022x^66+3168x^67+7212x^68+7586x^69+5436x^70+12138x^71+8232x^72+3840x^73+2592x^74+1090x^75+540x^76+258x^77+166x^78+114x^79+90x^80+18x^81+6x^83+4x^84

The gray image is a linear code over GF(3) with n=315, k=10 and d=183.
This code was found by Heurico 1.16 in 4.49 seconds.