Ferrite rod antenna for DCF77 simulator
Unfortunately a simple copper coil is used as an antenna, so the range of the signal generated is very limited,

Is that really so bad? Otherwise, you might/will get a very nice visit from the friendly people of the Autorità per le Garanzie nelle Comunicazioni. They might not be happy to see you.
You cannot just transmit where you want to. That's illegal.
Anyway, a ferrite rod is usually a very bad transmitting antenna, so this is taking you nowhere, to be honest.
Good transmitting antennas usually have to be in the size order of magnitude of the wavelength; for f=77 kHz, that's \$\frac{c_0}{f}\approx 4\,\text{km}\$. An antenna a couple hundred meters in size does work reasonable well. A part of the system that makes up the antenna looks like this:

So, honestly, close-range coupling is all you can and want to achieve. I'd honestly consider just putting small coils next to the devices you want to synchronize; feeding them from a central raspberry pi should be no problem, considering the low frequency.