The generator matrix

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

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+282x^65+202x^66+54x^67+774x^68+350x^69+756x^70+1866x^71+888x^72+2430x^73+4236x^74+1538x^75+2376x^76+2172x^77+420x^78+216x^79+564x^80+198x^81+288x^83+24x^84+24x^86+4x^87+20x^90

The gray image is a linear code over GF(3) with n=333, k=9 and d=195.
This code was found by Heurico 1.16 in 16.5 seconds.