The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+882x^69+1926x^70+1026x^71+2592x^72+2718x^73+1476x^74+2952x^75+2556x^76+774x^77+1506x^78+1062x^79+126x^80+62x^81+18x^84+6x^87

The gray image is a linear code over GF(3) with n=333, k=9 and d=207.
This code was found by Heurico 1.16 in 367 seconds.