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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+696x^153+486x^154+702x^155+1164x^156+432x^157+54x^158+916x^159+396x^160+54x^161+784x^162+288x^163+324x^164+222x^165+18x^166+18x^168+2x^186+4x^189

The gray image is a linear code over GF(3) with n=711, k=8 and d=459.
This code was found by Heurico 1.16 in 81.3 seconds.