You’ll need to enter your account via this link - https://cloud.digitalocean.com/login . From there you can actually reset the root password for your droplet if you don’t know it.
Once you are in, you can get to the DocumentRoot of your domain and use either Rsyc/SCP or FTP to download the code.
If you don’t know where is the DocumentRoot of your website, you can get it by following these steps :
First determine which Web Service you are using by executing the following command
netstat -tulpen | grep 80
It is most probably going to be either Apache or Nginx. Both should be located in the following directories /etc/apache2 or /etc/nginx. From there find your conf.d folder and go in. There you’ll see your website’s virtual configuration file. In it, you’ll be able to see the DocumentRoot