The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+108x^66+228x^67+324x^68+422x^69+1062x^70+1944x^71+1022x^72+2658x^73+3888x^74+1298x^75+2808x^76+2592x^77+678x^78+468x^79+78x^81+60x^82+10x^84+6x^85+14x^87+6x^90+6x^93+2x^96

The gray image is a linear code over GF(3) with n=333, k=9 and d=198.
This code was found by Heurico 1.16 in 0.63 seconds.