A319 Captain reported encountering wake turbulence climbing through FL260 from a preceding B777 that was 10-12 nm ahead of them.

Narrative

Encountered wake turbulence on climb thru FL260 on the way to FL370. It started as normal rumble of wake then quickly progressed. It was rolling the aircraft left and right; after initial roll I turned off the Autopilot. I attempted to dampen the rolling tendency while avoiding a PIO (pilot induced oscillation). There was no perceived pitch changes just roll. At times it seemed as if we were approaching roll limits for an upset. Best guess is It lasted about 30-45sec; I do feel time distortion could be a factor. After I got the roll controlled and maneuvered to the left; we noticed on TCAS there was only one aircraft in front of us. We contacted ATC; reported event and requested lateral maneuvering to the left of course to offset from traffic. Wind was a left quartering tailwind of about 55 kts. ATC stated a B-777 was ahead of us. At the time of incident it was 10-12nm ahead and 2500 ft above on the same course. We checked with the Flight Attendants (FAs) after regaining aircraft control. They stated they and passengers were OK. After the flight; the aft FAs were stunned and concerned during the event. They braced against passengers seats. They also stated the galley cart was moving side to side abruptly.