The generator matrix

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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+1302x^61+2112x^62+4984x^63+12264x^64+13278x^65+25676x^66+40062x^67+42300x^68+68114x^69+86208x^70+64938x^71+71990x^72+54420x^73+23202x^74+12028x^75+6810x^76+1386x^77+142x^78+96x^79+36x^80+36x^81+42x^82+6x^83+6x^84+2x^90

The gray image is a linear code over GF(3) with n=315, k=12 and d=183.
This code was found by Heurico 1.16 in 251 seconds.