A shake or shudder that only appears when you brake from highway speed - but not at low speed - is a classic symptom. It almost always traces to the rotors. Here is what causes brake vibration at highway speed.
Uneven rotor thickness
The usual cause is rotor thickness variation or uneven pad deposits. At high speed the rotor spins fast, so any thickness difference pulses the pad rapidly, and you feel it as a shudder; see warped rotor causes and why the pedal vibrates.
Why only at high speed
At low speed the same unevenness produces a slow, gentle pulse you may not notice. At highway speed the frequency rises into a shake you feel through the wheel or seat. That speed dependence is a strong rotor clue.
Front vs rear
Shaking felt mainly in the steering wheel points to the front rotors; a vibration through the seat or pedal points to the rear. The fronts do most braking and are the more common culprit.
How to fix
Resurface or replace the affected rotors in axle pairs, fit fresh pads, and bed them in properly to lay an even transfer layer; see breaking in brakes. Make sure wheels are torqued evenly. Fit quality pads and hardware.