Although we have the so-called option to limit the length of the title, the max length is actually set at 120:
'max_len_q_title' => 120,
qa-include / app / options.php
Update: Thanks Ansgar Wiechers for your answer. I'm building a Q2A site that resembles Who Wants To Be A Millionaire game, but most questions are about 140 characters long.
Admin → Posting → Maximum length of question title won't work because there is another interference of a Q2A builtin plugin called qa_filter_basic (or similar name). In other words, if you set the value greater than 120, it's still capped at 120. Of course, no choice but to override that plugin.