Why don't I have a design menu on my site?

I'm trying to make design changes to my site but for some reason there is no "design" menu in my site editor. I am one of three contributors on the site, so could it be a permissions issue? I can't find anything about this online and I have tried doing a hard refresh of the page, opening it in a different browser, and using a different computer, all to no avail. I'm adding a screenshot of what my home menu looks like. Help? 

This may be part of content editor access which does not have access to all parts of the site including settings, that level is admin. 

Yes, I checked with the site owner and they granted me access. Thanks!