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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+156x^121+360x^122+134x^123+306x^124+426x^125+342x^126+660x^127+1986x^128+578x^129+594x^130+408x^131+128x^132+114x^133+42x^134+2x^135+54x^136+84x^137+28x^138+24x^139+78x^140+30x^142+18x^143+6x^145+2x^177

The gray image is a linear code over GF(3) with n=576, k=8 and d=363.
This code was found by Heurico 1.16 in 50.6 seconds.