The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+372x^126+180x^127+180x^128+1512x^129+54x^130+144x^131+1872x^132+90x^133+1452x^135+90x^136+144x^137+360x^138+54x^139+18x^140+18x^142+14x^144+4x^162+2x^180

The gray image is a linear code over GF(3) with n=594, k=8 and d=378.
This code was found by Heurico 1.16 in 0.219 seconds.