Antenna coil resonant for 134.2KHz
You cannot make a resonant antenna for such low frequencies with those dimensions. Just try to calculate the wavelength for that frequency.

What is normally done (e.g. for RFID applications) is a RLC circuit that resonates at that frequency. The inductance L and part of R come from the coil; C and the rest of R are added components. Energy for transmission is normally provided by switching a transistor at that frequency. Be careful of the high voltages involved.