We are fighting some "terminology" issues ! I believe what the OP wants is a
beam that spans 20'
(without intermediate supports) and that he can then run
joists from a ledger on the back wall to the beam.
The way I read page 5 of
Eastern BCI and Vers-Lam Builder Guide that beam would have to be
at least a 6x16 LVL ! A steel beam might be cheaper and actually lighter ! Lally columns would be required at each end. Also these columns need to rest on a "full depth" concrete footing, not just the floor.
Joists should rest on
top of the beam or be attached with proper brackets
(NOT simply toe nailed). A ledger along the back wall for the joits to rest on is questionable. If that wall is just a 2x4 stud wall, the ledger should be supported down to the floor with edge-wise 2x6s, 24" O.C.