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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+258x^122+40x^123+294x^125+108x^126+732x^128+272x^129+2916x^130+1164x^131+242x^132+156x^134+22x^135+132x^137+30x^138+66x^140+6x^141+72x^143+2x^144+36x^146+4x^147+6x^149+2x^189

The gray image is a linear code over GF(3) with n=585, k=8 and d=366.
This code was found by Heurico 1.16 in 24.8 seconds.