The approach in the answer by Scuba Kay is technically possible but easy to get wrong. Small mistakes will cause the data to fail to unserialize correctly. You are better off “editing” the serialized data with PHP:
$str="a:4:{i:0;s:23:"bandpress/bootstrap.php";i:3;s:56:"posts-from-single-category-widget/post_from_category.php";i:4;s:15:"something else ";i:5;s:68:"syntax-highlighter-with-add-button-in-editor/syntaxhighlighterpp.php";}"; // copies from database
$strar = unserialize($str);
var_dump($strar); // find the key in the var_dump
unset($strar[4]); // remove the key you need to remove
echo serialize($strar); // copy and paste this back into the database
It is possible to do the same thing a bit more “automated” by using get_option and update_option.
But there are other ways to remove a stubborn plugin. The first that comes to mind, and simplest, is to use (s)FTP to just physically delete (or rename) the plugin file/folder from the wp-content/plugins directory.