The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1  1 2X^2+X  1  1  1  1 2X  1  1  0  1 2X  1 2X X^2+2X  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X+2 2X  1 2X^2+1  0 2X^2+2X+1  1  2 2X^2+X  1 2X+2 X+1 2X^2+X+2 2X^2+1  1  2 2X+2  1 2X^2+X  1  0  1  1 2X 2X^2+X X^2+X  2
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0  0  0 X^2 X^2 X^2  0 X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2 X^2 2X^2  0
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2  0 2X^2 2X^2  0  0 2X^2  0 X^2  0 X^2  0 X^2 2X^2  0 X^2 2X^2 X^2 X^2 2X^2
 0  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2 X^2 X^2  0 X^2  0  0  0 X^2 2X^2  0 X^2  0 2X^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+24x^61+84x^62+224x^63+282x^64+342x^65+1444x^66+1146x^67+612x^68+4906x^69+2232x^70+768x^71+4886x^72+1554x^73+522x^74+404x^75+96x^76+90x^77+16x^78+12x^79+12x^80+10x^81+2x^84+10x^87+4x^93

The gray image is a linear code over GF(3) with n=315, k=9 and d=183.
This code was found by Heurico 1.16 in 0.641 seconds.