The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+1710x^65+2568x^66+5544x^67+11892x^68+15204x^69+25020x^70+39942x^71+45654x^72+64674x^73+79338x^74+69834x^75+67572x^76+53520x^77+25728x^78+13482x^79+7248x^80+2018x^81+126x^82+222x^83+84x^84+36x^86+18x^87+6x^89

The gray image is a linear code over GF(3) with n=333, k=12 and d=195.
This code was found by Heurico 1.16 in 276 seconds.