Try this: create a plugin using hook location forumhome_start and code like this:
Code:
ob_start();
// insert code here without <?php or ?>
$backlinks = ob_get_contents();
ob_end_clean();
vB_Template::preRegister('FORUMHOME', array('backlinks' => $backlinks));
as the comment says, insert the code you posted above, but remove the <?php from the beginning and the ?> from the end.
Next, edit the FORUMHOME template and insert {vb:raw backlinks} where you want it to appear.
Edit: if you want step by step instructions for creating a plugin, see the vbulletin manual here:
http://www.vbulletin.com/en/manual/ . First select your vb version from the dropdown menu, then search for "plugin" and select "Adding or Editing a Plugin" from the results. It's pretty easy, you just have to paste the code I posted, then paste yours in at the comment and remove the <?php and ?>, then fill in the other form fields as needed (see the manual page for that). If you don't know what to put for something, you can probably leave the default.