Yes, you can, using same WP query as for any post type belonging to some taxonomy. Use code like this:
$args = array(
'post_type' => 'attachment',
'tax_query' => array(
'taxonomy' => 'your_taxonomy_slug_here',
'field' => 'id',
'terms' => 11 // your term ID here
$the_query = new WP_Query( $args );
while ( $the_query->have_posts() )
echo wp_get_attachment_image( get_the_ID(), 'thumbnail');
You can see your taxonomy slug and term id (id of the 'Banner Images' category) if you open 'Banner Images' for editing. In the URL you will see something like:
Here, 'document' is taxonomy slug and 11 is term id. If you use "Media Categories' that Enhanced Media Library created by default, then your taxonomy slug is 'media_category'.
Hope, this will help you.