The generator matrix

 1  0  1  1  1  1  1  0  1  1 2X^2  1  1  1  1 2X  1  1 2X^2  1  1  1  1  1 2X^2 X^2+X  1  1  1  1 2X^2+2X  1  1  1  1  X  0
 0  1  1  2 2X^2 2X+1 2X^2+2  1  0 2X^2+X+1  1 2X^2+X+2  0  2 2X^2+1  1 X+1 2X+2  1 2X^2  X X^2+2X+2 X^2+2X 2X^2+X+1  1  1 X^2 X^2+X+1 2X^2+X+1 2X^2+2X  1 2X^2+2X+1 2X 2X^2+2X 2X^2+X  1  X
 0  0 2X  0 2X^2  0 2X^2+X 2X 2X^2 2X^2+X X^2+X 2X X^2+2X  0 2X X^2+X  X 2X^2+2X X^2+X X^2+X X^2+X X^2+X X^2+2X X^2+2X X^2 X^2+2X 2X^2+2X X^2  X X^2+X  0 X^2+2X 2X^2 X^2 X^2+X X^2 2X^2+X
 0  0  0  X 2X^2+X X^2+X 2X^2 X^2 2X 2X X^2 2X 2X^2+2X 2X^2+2X X^2+2X 2X^2+X  0 2X^2 2X 2X^2 2X^2+2X X^2+X 2X^2 X^2+X 2X^2+X X^2+X X^2+X 2X^2 X^2+X X^2+2X X^2+2X  X 2X^2+2X X^2 2X^2+X 2X^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+810x^66+216x^67+1242x^68+2550x^69+1818x^70+4176x^71+6286x^72+5886x^73+8856x^74+9960x^75+6210x^76+5616x^77+3372x^78+450x^79+522x^80+810x^81+246x^84+18x^87+4x^90

The gray image is a linear code over GF(3) with n=333, k=10 and d=198.
This code was found by Heurico 1.16 in 87.7 seconds.