The generator matrix

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

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+612x^66+72x^68+1122x^69+324x^70+432x^71+3394x^72+1296x^73+3294x^74+5148x^75+1296x^76+576x^77+1188x^78+644x^81+252x^84+30x^87+2x^99

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 8.09 seconds.