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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+102x^123+480x^124+36x^125+450x^126+474x^127+486x^128+570x^129+1188x^130+864x^131+896x^132+492x^133+72x^134+74x^135+84x^136+36x^138+54x^139+44x^141+126x^142+6x^144+6x^147+18x^148+2x^177

The gray image is a linear code over GF(3) with n=585, k=8 and d=369.
This code was found by Heurico 1.16 in 0.425 seconds.