The generator matrix

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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+32x^57+42x^59+86x^60+174x^61+474x^62+102x^63+1182x^64+1842x^65+2528x^66+3402x^67+5754x^68+9802x^69+5502x^70+8580x^71+9790x^72+5340x^73+3234x^74+98x^75+378x^76+468x^77+64x^78+48x^79+18x^80+42x^81+12x^82+18x^84+20x^87+10x^90+6x^93

The gray image is a linear code over GF(3) with n=315, k=10 and d=171.
This code was found by Heurico 1.16 in 4.52 seconds.