The generator matrix

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

generates a code of length 37 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+80x^63+60x^64+78x^65+508x^66+150x^67+960x^68+2276x^69+1686x^70+5136x^71+5914x^72+6120x^73+10092x^74+7812x^75+6210x^76+6870x^77+4126x^78+258x^79+156x^80+276x^81+84x^82+36x^83+54x^84+12x^85+40x^87+38x^90+14x^93+2x^96

The gray image is a linear code over GF(3) with n=333, k=10 and d=189.
This code was found by Heurico 1.16 in 4.93 seconds.