Back in the day adioso.com did it but they haven't for years.
Many sites have the duration option (e.g. kayak's explore, skyscanner).
But I haven't found any sites that support this search function. It seems like a no brainer - who doesn't want to be able to plan their holidays around maximising weekend usage. I imagine there are probably technical issues with it like having to run 43+ searches for the one search (most flights are only bookable/searchable for up to 10 months/43 weeks in advance). But hot damn would it be handy.
Does it exist?
Adioso.com
Can. I just tried.