Add class to image's parent

function.php

function give_linked_images_class($html, $id, $caption, $title, $align, $url, $size, $alt = '' ){
  $classes = 'shutter'; // separated by spaces, e.g. 'img image-link'

  // check if there are already classes assigned to the anchor
  if ( preg_match('/<a.*? class=".*?">/', $html) ) {
    $html = preg_replace('/(<a.*? class=".*?)(".*?>)/', '$1 ' . $classes . '$2', $html);
  } else {
    $html = preg_replace('/(<a.*?)>/', '$1 class="' . $classes . '" >', $html);
  }
  return $html;
}
add_filter('image_send_to_editor','give_linked_images_class',10,8);