The ID can/should be given without quotes (otherwise if you a page with ‘38034’ as slug/post_name, this will be used instead of the page with the ID 38034). And you want to return $classes
no matter if you added your own or not.
add_filter('body_class', 'custom_body_class');
function custom_body_class($classes) {
if (is_page(38034))
$classes[] = 'new-class';
return $classes;
}