How to get access to the variables in Visual Composer extended WordPress plugin?

Solution:

From http://kb.wpbakery.com/index.php?title=Visual_Composer_tutorial:

This list represents shortcode tag as base and params list which will be editable with settings form inside js_composer constructor.

You must add the fourth_quote attribute to the shortcode.
For example:

public function renderMyBartag( $atts, $content = null) {

    # Also, avoid using extract()
    # http://stackoverflow.com/questions/829407/what-is-so-wrong-with-extract
    # http://codex.wordpress.org/Shortcode_API

    $a = shortcode_atts( array(
        'faa'          => 'something',
        'color'        => '#FF0000',
        'fourth_quote' => false, // just a default value
    ), $atts );

    $content = wpb_js_remove_wpautop($content, true);

    $output = $a['fourth_quote'];

    error_log(date('[ d.m.Y H:i:s ] ') . $output . PHP_EOL, 3, "my-errors.log");

    return $output;
}