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

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+720x^69+2220x^70+1458x^71+1746x^72+2634x^73+2034x^74+2460x^75+2718x^76+1278x^77+1116x^78+1128x^79+90x^80+26x^81+30x^82+6x^84+18x^85

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 47.3 seconds.