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 2X^2+2X  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 2X+2  0 X^2+X+1 X^2+X  X X^2
 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+1  1 X^2+2X+1 2X^2+2 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 2X^2 X^2 X^2  0 2X^2 2X^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+774x^67+1116x^68+1808x^69+4284x^70+3504x^71+4666x^72+9120x^73+6864x^74+7730x^75+8898x^76+4368x^77+2452x^78+2556x^79+654x^80+74x^81+96x^82+12x^83+28x^84+30x^85+6x^86+6x^87+2x^90

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 10.7 seconds.