You should check out the WordPress function do_shortcode()
.
You can use it to generate the shortcodes, in a string variable, like this :
<?php echo do_shortcode( $content ) ?>
So in your case, please try:
<?php
if ( of_get_option('footer_contact_form') ) {
echo do_shortcode( of_get_option('footer_contact_form') );
}
?>