Drupal site is compromised by backdoor My Drupal site has been compromised. 

Although I applied all modules updates and update my Drupal core to 7.35, it is still compromised.

What would the next logical step to take be?
Sorry to hear that. The steps you should take are as follows:


If you have drush access, install drupalgeddon by typing drush dl drupalgeddon.
Run drush drupalgeddon-test. You will likely find several accounts which you did not create. Remove them.
Install hacked to find out which (if any) files have been changed.
Read this article.