grep is going to be working on a line by line basis, so grep ^09 is doing just what you asked it to do by finding any line that begins with 09

You probably want to use awk, it would be the easiest thing to do. If the data is in the same format that you provided, you could do something like the following:

awk '$4 == "0000001234"' file

-bash-3.2$ cat test.txt
09 0 XXX 0000001234 Z 1
09 0 XXX 0000001234 Z 1
09 0 XXX 50000001234 Z 1
09 0 XXX 40000001234 Z 1
09 0 XXX 30000001234 Z 1
09 0 XXX 10000001234 Z 1

-bash-3.2$ grep "\<0000001234\>" test.txt
09 0 XXX 0000001234 Z 1
09 0 XXX 0000001234 Z 1