this is probably the wrong place to ask, only because what you're looking to do is more of a radio thing, and not a car topic per-se. SDR, or Software Defined Radio has been making headlines in different circles for ease of access, it might be an option here.
ought to just need the frequency of the remote, which should be obtainable through the FCC id, which is HYQ14ACX, and then start looking into the SDR forums for a directional antenna and reciever.
https://www.sdr-radio.com/
all i really know is that it exists. i don't really know how or where to use it...
but then an SDR setup is likely going to cost around $200-400.
another option might be to get in touch with some local HAM Radio groups. tell them you need help with a treasure hunt. many of them likely already have the equipment needed. of the guy's i know that do it, they'd do it for a good meal, and for fun...