The value of $post_id depends on what version of ACF you are using.
In ACF 4 or < 5.5.0
$image = get_field('cck_menu_category_image', $category->taxonomy.'_'.$category->term_id );
In ACF >= 5.5.0 you can use the above or you can use
$image = get_field('cck_menu_category_image', 'term_'.$category->term_id );
I think that you might also be able to use (but I’m not sure)
$image = get_field('cck_menu_category_image', $category);