Try a 4040 or similar, perhaps? 12 bits, and some implementations can run at 200 Mhz. You can daisy-chain two to get a 24 bit counter, although interfacing to the Arduino then may need multiplexing.
However, you'd need to generate that 200 MHz pulse train yourself, probably using a crystal and an amplifier/inverter circuit.
Also, you'd need to wire up the right circuit to gate the counter clock while the pulse is on, and then interrupt the Arduino once the pulse completes, so you can read the value and reset the counter. Probably want to use flip/flops to lock out multiple additional triggers until the count has been reset.
Finally, at 200 Mhz, the circuit board design starts mattering. You may run into signal quality issues if you're not careful. You probably want to use surface mount manufacture, and you quite likely can't build this very well on breadboard type surfaces at all.