Ruger 77 Models, that I've ever seen, use a prietary(sp) Ring system, so if there is a Base Mount, then I would be suspicious. I have seen Mounts that are built specifically for the 77 Models to change to a Weaver Ring Mount system, so this might be what you have.
First, take Rifle and look at total package from the side. Does Scope look to be on a level with Receiver/Barrel? Or does Scope appear to be pointed upwards?
If there is any angling of Scope, does it appear to be coming from the Rings or Base Mount? I'm thinking the Base is your problem. Can it be turned around to realign the Scope?
I will say, one time I got some Weaver Medium Rings and they were packaged incorrectly, as one ring was just a couple mm's taller than the other, and really threw off my 30-06.
Just pulled out my 77/22 Magnum and yes, (Factory Rings) are same heigth, which are the Medium/Tall model I believe. I have a 3-12x44mm Scope on it and there's at least 1/4" Barrel clearance. If you also have a Mount and Rings on top of the Factory Ring Mount, then your Scope may be too far above the Barrel and this is where you may be having troubles of getting Barrel to come up high enough. Get some Short Rings(bring Scope closer to Barrel) to see if this will cure your problem.