The generator matrix

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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+726x^124+1320x^125+1674x^126+2460x^127+1908x^128+1470x^129+1740x^130+1602x^131+1286x^132+1716x^133+1290x^134+756x^135+756x^136+522x^137+234x^138+186x^139+4x^141+24x^142+2x^144+6x^145

The gray image is a linear code over GF(3) with n=585, k=9 and d=372.
This code was found by Heurico 1.16 in 1.22 seconds.