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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+372x^59+454x^60+1848x^61+3336x^62+5180x^63+8532x^64+11442x^65+16982x^66+22704x^67+24528x^68+27774x^69+23862x^70+15318x^71+8326x^72+4122x^73+1698x^74+280x^75+138x^76+156x^77+50x^78+30x^79+12x^80+2x^81

The gray image is a linear code over GF(3) with n=306, k=11 and d=177.
This code was found by Heurico 1.16 in 30 seconds.