The generator matrix

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

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+90x^57+180x^59+270x^60+1740x^62+748x^63+1458x^64+8580x^65+1684x^66+5832x^67+16878x^68+2192x^69+5832x^70+11436x^71+1236x^72+492x^74+190x^75+60x^77+74x^78+38x^81+34x^84+2x^87+2x^90

The gray image is a linear code over GF(3) with n=306, k=10 and d=171.
This code was found by Heurico 1.16 in 4.56 seconds.