It happens, now first thing you need to do is restrict your site to be access only through your IP using .htaccess file.
take backup of .htaccess file and add this below code in .htaccess
credits :TBI InfotechTBI Infotech for this linkthis link
order deny,allow
deny from all
allow from 111.222.333.444
There are lot of resources available to remove hacking code here , if that did't works for you,
next thing is as you said you have backup , than revert to previous backup. than scan you site in Magereport . there they will mention to install required security patches and changing admin and magento connect url . once you install security patches , than lot of 3 -party extensions feature may break down. you need to contact extension team to provide updated extensions that supports security features.
or if you don't have any 3-part modules , if you did't done any core files edit [ also if you are struggling to install all security patches ] , than upgrade to 1.9.2.4 version