The generator matrix

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

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+746x^147+648x^148+1662x^150+504x^151+842x^153+324x^154+1124x^156+432x^157+228x^159+36x^160+8x^162+4x^180+2x^192

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 10.9 seconds.