All the answers above are great. I would just like to add that, if you plan to publish it on your lab's website or any personal website, you should also copy it somewhere else.
In many fields, it appears that data (including original programs) is disappearing all the time. When a lab moves to another University, closes, or undergoes any kind of restructuration, its website is likely to change, and data stored there can be lost. So, unless your University has a centralised repository, you should put your code where it can stay for decades, for instance on Github.