Try with error.log and access.log, the others with the numbers are old logs.
tail -n 20 error.log
This will display the last 20 lines of that file, if you don't see anything particular, reload the page in the browser. If you need to all the file type:
If needed do the same with access.log. Then if you don't find anything browse to /etc/apache2/sites-available/ and open the file configuration of your virtual host, from there you can see if your configuration is saving the errors into another path, the line should look like:
You can also try to find if CodeIgniter is generating an error log.
Ok, it seems related to permissions. You should check the user running Apache (usually www-data) and switch the ownership of the files and subdirectories of /var/www/code to it, run this:
ps -aux |grep apache2
to see the user, the parent is root, all the child processes should be owned by www-data or another defined user in /etc/apache2/apache2.conf, and then change the ownership:
sudo chown www-data:www-data -R /var/www/code
If this still does not work, then change the write permissions:
sudo chmod 755 -R /var/www/code
Note that 755 works if the owner of the files is the same user used by Apache, otherwise you need to use 777, which can be fine in a development box, but it is not good in a production server. Hope this helps to solve the problem.