Yes, you can! I started studying web development at the beginning of last year, which is 27 and got my first developer job in Oct 2017. Although the result is not so good…
I quit and tried to land other jobs afterwards, after few months (Dec 2017), I got an offer at bank for updating simple HTML pages. And now (Aug 2018), I finally get a job titled “Front end developer” in a well-known company!
Nothing is impossible! I believe you can also become a developer!