This answer is an extension to @raphadko's answer.
If you need to extract manually the captcha code (like in ajax requests) you have to call:
grecaptcha.getResponse(widget_id)
But how can you retrieve the widget id parameter?
I use this definition of CaptchaCallback to store the widget id of each g-recaptcha box (as an HTML data attribute):
var CaptchaCallback = function() {
jQuery('.g-recaptcha').each(function(index, el) {
var widgetId = grecaptcha.render(el, {'sitekey' : 'your code'});
jQuery(this).attr('data-widget-id', widgetId);
});
};
Then I can call:
grecaptcha.getResponse(jQuery('#your_recaptcha_box_id').attr('data-widget-id'));
to extract the code.