The generator matrix

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

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+1002x^59+1964x^60+5562x^61+10200x^62+13794x^63+26172x^64+37440x^65+47516x^66+69042x^67+76962x^68+75520x^69+72354x^70+49734x^71+24206x^72+13356x^73+5256x^74+940x^75+114x^76+192x^77+78x^78+24x^79+6x^80+6x^81

The gray image is a linear code over GF(3) with n=306, k=12 and d=177.
This code was found by Heurico 1.16 in 242 seconds.