Just to clarify the situation, there is no such thing as a generic family Coat of Arms for the name Plowman. Certain individual Plowman have been granted Arms for their use and that of their descendants. Unless you can prove direct male descent from the grantee, you cannot use those Arms.

The results of a search done by the College of Arms, London, can be viewed at:

http://homepage.ntlworld.com/stephen.plowman1/search.html