The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+232x^147+1194x^148+660x^149+394x^150+996x^151+450x^152+254x^153+768x^154+390x^155+230x^156+684x^157+108x^158+90x^159+72x^160+6x^161+6x^169+6x^170+10x^171+6x^175+2x^177+2x^180

The gray image is a linear code over GF(3) with n=684, k=8 and d=441.
This code was found by Heurico 1.16 in 0.304 seconds.