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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+196x^120+90x^121+18x^122+252x^123+294x^124+108x^125+186x^126+732x^127+3132x^128+214x^129+714x^130+144x^131+136x^132+36x^133+74x^135+24x^136+72x^138+6x^139+40x^141+48x^142+36x^144+2x^147+4x^150+2x^183

The gray image is a linear code over GF(3) with n=576, k=8 and d=360.
This code was found by Heurico 1.16 in 0.364 seconds.