How do you pipe after a here document

[afsipmh at cidsv01.cid.aes.doe.CA]

 I want to do something like the following:

#! /bin/sh
cat <<END
I,ve got
a lovely
bunch of coconuts
END 
| grep coconuts

The above doesn't work so how can I do it?
-- 
Pat Hertel                 Canadian Meteorological Centre
Analyst/Programmer         2121 N. Service Rd.        % rm God
phertel at cmc.aes.doe.ca     Dorval,Quebec              rm: God non-existent
Environment Canada         CANADA           H9P1J3