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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+128x^126+36x^127+78x^128+126x^129+1554x^130+60x^131+64x^132+24x^133+24x^134+54x^135+6x^136+30x^138+2x^195

The gray image is a linear code over GF(3) with n=585, k=7 and d=378.
This code was found by Heurico 1.16 in 0.113 seconds.