First of all, I think we need to clarify things. The Grey Havens are the harbours in Middle Earth from where the boats to Valinor leave. Valinor, in Aman is the holy land, the undying land.

Anyway, if Gimli was allowed in, then why not Hurin? Why not Tuor? Why not Turin? (well.....maybe not Turin.....). But Hurin and Tuor? Their actions far out-shadowed those of the Fellowship. I'd bring Beren into this, but that went in a totally different direction.