For the added members, you can create another file that contains another partial of the class. This new file won't be overwritten so anything you've added there should persist between updates.
For the changes that aren't new members (like the added line in the constructor), you can edit the Model.Context.tt file directly. This is a simple T4 Text Template used to re-generate the code when the model is updated. It is similar to an ASP.NET page; however, instead of using C# to generate HTML, it uses C# to generate more C#.