The 60kHz is too high for the Arduino.
Perhaps it is possible to sample 8-bits at that rate, but there is not time to do something with it. Perhaps it is possible with highly optimized code.
You would need extra hardware for the serial output. 60kHz sample rate * 8 bits = 480kHz. So you need a clock of 480kHz to output the serial bits.
60kHz is not the lowest frequency to transmit. Submarines use lower frequencies.
Do you want to use the 60kHz clock (digital clock) to transmit ? The digital clock is a square wave, you would perhaps transmit more power into the harmonics than the original 60kHz.