Not working with my Graphene Theme

I have a featured image for all of my posts and pages, but have been unable to figure out how to set a default for the homepage of the website. I selected an image to use, but whenever I try to tweet a link to it, no image shows up at all. I’m using the graphene theme. I’ve also tried setting a default image in JM Twitter Cards, but nothing I do will create an image for the site url (homepage). Any ideas? Thanks.

The page I need help with: [log in to see the link]