Fallback media image for featured image not working in admin column

wp_get_attachment_image_src(156, 'archive_thumbnail')[0] will only echo the URL of the image. You need to add it to html to display the image. Try this:

echo '<img src="'.wp_get_attachment_image_src(156, 'archive_thumbnail')[0].'"/>';

You could add the width etc as well

echo '<img src="'.wp_get_attachment_image_src(156, 'archive_thumbnail')[0].'" width=".wp_get_attachment_image_src(156, 'archive_thumbnail')[1]." height=".wp_get_attachment_image_src(156, 'archive_thumbnail')[2]." />';

what happens if someone deletes this image though? Do you have a fallback?

It may be better to add the fallback image to your theme or plugin directory and reference it that way.

UPDATE
If you just want to add the image as simply as possible. You could also try this:

wp_get_attachment_image( 156, 'archive_thumbnail' );