Although you're using the term 'antenna', to nature it is simply an inductor.
For transmit mode, to increase the magnetic field output you need to increase the amp-turns. The simplest way to do this is probably to add more turns, but at some point the inductance may impede your "high frequency" ;-) signal.
I would design & treat the transmitter as a current source.
For receive mode, the optimum coil might well be different. In general, I think that you can use many more turns.
You don't necessarily need to match impedance for receive mode because the signal-to-noise ratio (SNR) at these frequencies is almost certainly set by the external environment (not the amplifier input).
Careful filtering might be essential.
Another thing that might be possible (depending upon how much time you have) would be to repeat the measurement and synchronously add-up the return signal. If the target is in 'the zone' for ten pulses, then a 10:1 (10dB) SNR improvement should be possible.
Note - all above is based on what I know about LF communications systems. I believe it is applicable, but stand-by for any corrections from others.