display custom post type in widget aera

You dont have to make a post type Contact.Just make a dynamic sidebar in the Widget area of WordPress.And take the Text Widget in that Dynamic Sidebar , Copy your html and Paste it there in the Dynamic Widget Area you make. If you are not able to make the Dynamc sidebar Paste ths code in you functon.php

    register_sidebar( array(
    'name'          => __( 'contact_sidebar', 'twentythirteen' ),
    'id'            => 'sidebar-4',
    'description'   => __( 'Appears on posts and pages in the sidebar.', 'twentythirteen' ),
    'before_widget' => '',
    'after_widget'  => '',
    'before_title'  => '<h2>',
    'after_title'   => '</h2>',
) );

Then call it on your footer.php by

<?php dynamic_sidebar('sidebar-4');?>