The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+618x^67+1422x^68+2088x^69+3114x^70+4614x^71+5562x^72+5946x^73+8436x^74+9548x^75+6432x^76+5478x^77+2916x^78+1728x^79+876x^80+44x^81+120x^82+60x^83+8x^84+24x^85+12x^86+2x^93

The gray image is a linear code over GF(3) with n=333, k=10 and d=201.
This code was found by Heurico 1.16 in 97 seconds.