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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+108x^128+98x^129+318x^130+192x^131+726x^132+456x^133+132x^134+38x^135+24x^136+24x^137+14x^138+12x^139+30x^140+12x^141+2x^192

The gray image is a linear code over GF(3) with n=594, k=7 and d=384.
This code was found by Heurico 1.16 in 0.119 seconds.