The generator matrix

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

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+286x^69+150x^70+738x^71+1176x^72+324x^73+1314x^74+840x^75+282x^76+684x^77+644x^78+36x^79+6x^80+30x^81+6x^82+6x^83+18x^84+12x^85+6x^86+2x^99

The gray image is a linear code over GF(3) with n=333, k=8 and d=207.
This code was found by Heurico 1.16 in 0.0752 seconds.