I have used the following without success. The active workbook closes, indeed, but the excel window remains open.
Application.ActiveWindow.Close SaveChanges:
Application.Quit
Should do the trick.
I think your problem is that it's closing the document that calls the macro before sending the command to quit the application.
Your solution in that case is to not send a command to close the workbook. Instead, you could set the "Saved" state of the workbook to true, which would circumvent any messages about closing an unsaved book. Note: this does not save the workbook; it just makes it look like it's saved.
ThisWorkbook.Saved = True
and then, right after
Application.Quit