Exposed NM wire in unfinished garage walls

[Unregistered]

I understand that you cannot run NM wire horizontally in an unfinished garage wall without protection. I would like to go horizontally because this garage has tall walls. I plan to nail a short 2X4 vertically between each stud space for protection and staple the wire to that mid way between studs. my question is, can I run the NM wire across the face of that 2X4 or does it need to be nailed to the under side of it? I am thinking face might not be considered protected from having ladders or other stuff leaned against the wall.