The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+600x^61+804x^62+1776x^63+4614x^64+3198x^65+5280x^66+8652x^67+5820x^68+9732x^69+9504x^70+3780x^71+2370x^72+2280x^73+456x^74+30x^75+96x^76+30x^77+6x^78+12x^79+6x^80+2x^81

The gray image is a linear code over GF(3) with n=306, k=10 and d=183.
This code was found by Heurico 1.16 in 3.62 seconds.