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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+192x^146+142x^147+348x^149+150x^150+648x^152+54x^153+2916x^154+1362x^155+270x^156+150x^158+48x^159+2x^162+66x^164+150x^167+54x^168+6x^171+2x^228

The gray image is a linear code over GF(3) with n=693, k=8 and d=438.
This code was found by Heurico 1.16 in 81.1 seconds.