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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+70x^153+72x^154+108x^155+1728x^156+72x^157+54x^158+54x^159+18x^160+8x^162+2x^234

The gray image is a linear code over GF(3) with n=702, k=7 and d=459.
This code was found by Heurico 1.16 in 0.209 seconds.