I am a non-EU citizen software developer, which means I should be considered highly skilled migrant practically everywhere in the EU.

I want to move to Czech Republic (my girlfriend lives there as a non-EU student/researcher), but there are more jobs (and more good jobs) for me in, for example Germany or The Netherlands. Some of these companies allow working remote, so I was wondering if it is legally possible for me to work for, let's say, German company (and thus acquire a German working permit) and reside in Czech Republic?