The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X^2  X  1  1  1 2X^2+2X  1  1  1  1  1  1  1 2X  1  1  1  1  0  X X^2+2X  1  1
 0  1  1  2 2X^2+2X+1 2X^2 2X^2+2  1 X+1 2X^2+X 2X+2  1  1 2X^2+2X+1 2X^2+X+2 2X  1 2X^2+X+1 2X^2+2X 2X^2+X X+2  1 2X+2 X+2  1  0 2X^2+X+2 2X 2X^2+1 X^2  1  1 X+1 X+1
 0  0 2X  0  0 2X^2+X 2X^2+X 2X^2 X^2 2X^2+2X X^2+2X 2X^2+X X^2+X 2X 2X^2+2X X^2+2X 2X^2+X 2X^2+X  X 2X^2 2X^2+X X^2+X X^2  X 2X 2X^2 X^2  0  0  X  X 2X 2X^2+2X 2X
 0  0  0 X^2  0 2X^2  0 X^2  0  0 X^2 2X^2 2X^2  0 2X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 2X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2  0  0 2X^2
 0  0  0  0 2X^2  0  0  0 X^2  0  0 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2  0 X^2  0 X^2 2X^2 2X^2 X^2 X^2  0  0 2X^2 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+162x^59+420x^60+234x^61+1440x^62+1608x^63+1656x^64+5742x^65+5832x^66+5292x^67+10704x^68+8510x^69+5382x^70+7476x^71+2974x^72+558x^73+540x^74+252x^75+168x^77+68x^78+12x^80+12x^81+2x^87+4x^90

The gray image is a linear code over GF(3) with n=306, k=10 and d=177.
This code was found by Heurico 1.16 in 20.4 seconds.