What is the altitude record for a turbofan? The (usually) turbofan-powered U2 has gone to 74,000 ft (22.6 km) MSL, but did any turbofan plane surpass that, in a zoom climb for instance and with afterburners' help?
In 1975, the F-15A Streak Eagle, propelled by 2 afterburning turbofans, climbed to 98,425 feet in 3½ minutes, coasting nearly up to an altitude of 103,000 feet.
I am not entirely certain where you have your information from. The U2's service ceiling was 70.000 feet and I can't find any reports about it going higher.
The F-104 mentioned in @bjelleklangs answer uses a turbojet engine so that disqualifies it from your question. The F-15A Streak Eagle mentioned in @Bob Mathews answer would be a valid contender but I want to mention the McDonnell Douglas F-4 Phantom, which had turbofan variants for the Royal Navy and the Royal Air Force and reached an official maximum height off 98.557 feet a tad bit higher than the F-15. Most likely not with the correct variant though.
Both these planes definitely used afterburners. The highest altitude ever reached by a plane simply powered by a propeller, which is a category I would put turboprops under, without an afterburner was NASA's Helios HP01 at 96.863 feet.