This is more an Outlook topic than a Word one, however the following Outlook
code should do the trick.
Note that the extra wdWindowState lines ensure that Word opens in front of
Outlook. If Word is already running it will use that rather than open
another instance. The extra unused code at the end closes Word after running
any processes where indicated. Ensure that the Word Object Library is
checked in the vba references.

Sub OpenWord()
   Dim wdApp As Word.Application
   Dim wdDoc As Word.Document
   Dim WordWasNotRunning As Boolean
   Dim strMyTemplate As String
   strMyTemplate = "D:\Template Path\Template Name.dot"

   WordWasNotRunning = False
   On Error Resume Next
   Set wdApp = GetObject(, "Word.Application")
   If Err Then
       Set wdApp = CreateObject("Word.Application")
       WordWasNotRunning = True
   End If
   Set wdDoc = wdApp.Documents.Add strMyTemplate

   wdApp.WindowState = wdWindowStateMinimize
   wdApp.Visible = True
   wdApp.WindowState = wdWindowStateNormal

  ' do whatever else you want here -e.g. wdApp.Run YourWordMacro etc.

   ' and when you're finished
   'If WordWasNotRunning = True Then
   '    wdApp.Quit
   'End If
   Set wdDoc = Nothing
   Set wdApp = Nothing
End Sub