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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+330x^146+304x^147+678x^149+684x^150+234x^151+1170x^152+1538x^153+1404x^154+2010x^155+2978x^156+2322x^157+1902x^158+1938x^159+414x^160+390x^161+250x^162+330x^164+100x^165+246x^167+90x^168+144x^170+86x^171+66x^173+36x^174+18x^176+6x^177+6x^179+6x^180+2x^210

The gray image is a linear code over GF(3) with n=702, k=9 and d=438.
This code was found by Heurico 1.16 in 27 seconds.