For doing code reviews, you should be an expert in that code base. So you should have a fair idea of critical parts of the code. For example, details of logging may not be as important as say a new data structure being introduced. So if you have to skim some parts, skim over the less critical parts.
In languages like C or C++, starting with header file changes give an idea of significant changes. The key is data structure changes. New data structures added, new fields added to existing data structures etc. You can ask the implementor for details of data structural changes.
Also being an expert in the code base, you should have a fair idea of newbie mistakes that can happen. You can even document such easily made mistakes and use it as a check list. Others also will find it useful. Maybe it can be part of an internal wiki.