The generator matrix

 1  0  0  1  1  1  1  1 2X  1 2X^2+X  1  1  1 2X  1  1  1  X 2X^2+2X  1  1  1 2X  X  1  1  1  1  1  1  1  X  1  X
 0  1  0  1 2X^2+2X 2X^2+2  1 2X^2+2  1 2X+2  1 X+1 2X^2 2X^2+2X+1  1  0 X^2+2X 2X^2+2X+2 2X^2+2X  1 2X^2+1 2X+1  2  0  1 X^2+X X+2 2X^2 X^2+2X+1 2X 2X^2+2X+2 2X^2+2X+1  1 X^2+2X 2X^2+2X
 0  0  1  2 2X^2+2X+1 2X^2+X+2  1 2X^2+X 2X^2+X+1 2X+1 2X^2+2X+2 2X 2X^2+2X+2 2X^2+2X+2 2X^2+X 2X X^2+2 2X^2+X+1  1 2X^2+2X+2 X+1 2X^2+2X X^2+X+2  1  1 X^2+2 2X 2X^2+2X+1  1 2X^2+X+1 X^2+2X+2 2X^2+X+1 X+1 2X^2+1 2X^2+X
 0  0  0 2X 2X^2+2X 2X 2X^2  0 X^2+2X X^2+X X^2+2X X^2 2X^2+X 2X^2 2X^2+X 2X^2+2X  0 2X^2 X^2+X  X 2X^2+X  X  X X^2+2X  X  X X^2+X X^2+X 2X X^2  0 X^2+X X^2 2X^2+2X X^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+432x^61+726x^62+1898x^63+3972x^64+5388x^65+7902x^66+13560x^67+16866x^68+20388x^69+23988x^70+26988x^71+20884x^72+17820x^73+8700x^74+4366x^75+2334x^76+522x^77+180x^78+96x^79+96x^80+26x^81+6x^82+6x^83+2x^84

The gray image is a linear code over GF(3) with n=315, k=11 and d=183.
This code was found by Heurico 1.16 in 31.2 seconds.