The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+56x^57+114x^60+124x^63+102x^66+5832x^68+86x^69+58x^72+46x^75+62x^78+60x^81+10x^84+8x^87+2x^102

The gray image is a linear code over GF(3) with n=306, k=8 and d=171.
This code was found by Heurico 1.16 in 0.175 seconds.