The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  0  1  1  1  1  1  1  X  X  1  1  X  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X 2X^2+X X^2+2X  0 2X^2+X X^2+X X^2 2X^2+X 2X  X  0 2X^2+X  0  X X^2+X 2X^2 2X^2+X 2X X^2+X 2X 2X^2+X X^2+2X  0  0
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 X^2 X^2  0 X^2  0  0 2X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2 X^2 X^2 2X^2  0  0
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 X^2 X^2  0  0 X^2 2X^2 2X^2  0 X^2 X^2  0  0 2X^2 X^2 X^2 2X^2 X^2 X^2 2X^2  0  0
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2 2X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 2X^2 2X^2  0  0 X^2  0 X^2  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+46x^57+216x^60+36x^61+84x^62+372x^63+252x^64+138x^65+1100x^66+1332x^67+1902x^68+2572x^69+2394x^70+3318x^71+2728x^72+1692x^73+294x^74+538x^75+126x^76+96x^77+322x^78+54x^81+42x^84+22x^87+4x^90+2x^93

The gray image is a linear code over GF(3) with n=315, k=9 and d=171.
This code was found by Heurico 1.16 in 1.01 seconds.