The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  0  X  1  0  1  1  1  1  X  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X X^2+X X^2+2X  0 X^2+X  0 2X 2X^2+X X^2 X^2+2X 2X^2 2X^2 2X^2+X 2X^2+X X^2+2X 2X  X 2X^2+X 2X  X X^2+X X^2  0 X^2 X^2 X^2+X
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 X^2  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0 X^2 2X^2  0  0 2X^2  0 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 2X^2  0  0  0 X^2  0 2X^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+172x^63+54x^64+24x^65+328x^66+144x^67+132x^68+492x^69+1206x^70+312x^71+2026x^72+4230x^73+462x^74+3822x^75+4212x^76+408x^77+692x^78+252x^79+120x^80+282x^81+90x^82+102x^84+18x^85+56x^87+30x^90+14x^93+2x^96

The gray image is a linear code over GF(3) with n=333, k=9 and d=189.
This code was found by Heurico 1.16 in 1.74 seconds.