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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+86x^117+162x^119+194x^120+510x^122+304x^123+1020x^125+828x^126+3492x^128+2202x^129+5586x^131+2268x^132+1662x^134+282x^135+498x^137+182x^138+108x^140+58x^141+72x^143+78x^144+6x^146+22x^147+6x^149+30x^150+8x^153+8x^156+4x^159+4x^162+2x^174

The gray image is a linear code over GF(3) with n=585, k=9 and d=351.
This code was found by Heurico 1.16 in 2.34 seconds.