How do I improve a paper if they haven't published any code?
Even though journals encourage authors to publish their code and make their research easily reproducible, in some fields most authors do not publish their code. 

In many cases, publishing code is plenty of extra work with little immediate benefit, as one would have to comment it/improve readability and check all licensing requirements of possibly reused snippets. There is often little motivation to do all this extra work on code that is anyway evolving in the middle of a project. In addition, publishing your code takes away your head start and enables the whole world to beat you to your own "future work" plans, so people might tend to only publish code when a project is finished. 

This unfortunately means that you often have to implement state-of-the-art algorithms to be able to improve them or prove that you can beat them. Ideally, the algorithm is completely and unambiguously explained in the paper, so you should be able to implement it. Practically, this is not always the case, but you can always contact the corresponding author of the paper and ask for clarification. There is a reason why most articles include contact information of the corresponding author.