The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X^2+2X X^2 2X^2  1 2X^2 2X  1  1  1  1  1  1 2X^2+2X  1  1  1 2X  1  1  1 X^2  1  1 2X  1  1  1  1  1  1  1  1 2X  1  1  1  1  1 2X^2+2X  1  1  1 2X^2+X  1  1 X^2  1  1 2X^2+2X  0  1  X X^2+2X  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2  2 2X^2+2X+2 X^2+2X+1 X+1  1  1  1 2X^2+2X+1  1 2X^2+2X X^2+X+1  2 2X^2+1 2X^2+2 X^2+X+2  X  1 X^2+X X^2+X 2X+2  1 2X^2+1 X^2 X+2  1 2X+1 2X^2+X+1  1 2X^2+X+2 2X^2+2X X^2+2X+2  0 2X^2+X+2 X^2 2X^2+X+1 X^2+1 X^2+X X+1 X^2+1 2X^2+X X^2+2X X^2+2X+2  1 2X^2+2X  1  0  1 2X^2+1 X^2+2X+1  1 X+2 2X+2  1 2X 2X^2+X+1  X  1 2X
 0  0  1 2X^2+2X+1 2X^2+2 X^2+2 2X^2+X+2 X^2 X^2+2X+1 X+1  0 2X+1 2X^2+2X+2 2X^2+2X+1 X^2 2X^2+X  1 2X^2+2 X^2+2 2X^2+X+1 2X^2+X 2X^2+X+1 2X+1 2X^2+X+2 X^2+X+2 2X^2+2X X^2+2X 2X+2 2X+1 X+2 2X^2+X+2 X^2+1 X^2+X+2 2X X^2  1 2X^2+2X+1  1 2X X^2 X^2+1 2X+2 X^2+2X  1 2X^2+1 X^2+X  0 X^2+X+2 X^2+X 2X^2 2X+2 X+1 2X^2+X X^2+2X+1  1 X^2+X X^2 2X  2 2X  1  2  1 X^2+X X+1
 0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 2X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2 2X^2  0 2X^2  0  0  0  0 2X^2 X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2 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+654x^122+1556x^123+1890x^124+3510x^125+4062x^126+4344x^127+5238x^128+5854x^129+5274x^130+5784x^131+5138x^132+4206x^133+4374x^134+3252x^135+1482x^136+1206x^137+732x^138+270x^139+78x^140+44x^141+24x^142+36x^143+8x^144+18x^146+8x^147+6x^154

The gray image is a linear code over GF(3) with n=585, k=10 and d=366.
This code was found by Heurico 1.16 in 7.51 seconds.