Here is a different solution, which may or may not be easier to build and work with.
The idea here is to build a whole amplifier for the signal from the piezo transducer, and then just brutally clipping/limiting the signal amplitude at critical points in the signal path. This way you can build an amp, which has more than adequate gain, and you will get a fairly reasonable and constant amplitude square wave/PWM signal out, regardless of input signal strength.
*) You may need more gain stages than I could be bothered to draw, probably one and maybe even two additional stages. Copy everything in the schematic below from and including C4 and back to the input, and attaching as many duplicates as needed.
*) The voltage gain of each stage is about 12. The gain of for instance U1a has a set gain of (1 + R3/R2) ~ 13, but this is reduced by the voltage divider made up by R4/R5. So for 3 gain stages the total voltage gain would be ~ 1700.
*) Now imagine you have 3 or 4 gain stages and the input signal is very strong. Maybe the output signal at pin 1 of U1a would then be, say, +/- 5V. What happens now is that D1 and D2 starts to conduct as soon as the voltage across the pair is above/below roughly 0.65V. R4 limits the current through the diodes to something reasonable U1a can cope with. The +/- 5V signal has now been 'cut down' to a fairly nice +/- 0.65V square wave (1.3V peak-to-peak amplitude). This signal is amplified once again by U1b, boosting it to +/- 8.5V, which now appear at pin 7.
R8 plus D3 now clips the signal again, making an asymmetric -0.65 / +4.7 V square wave-ish signal. The Signal to the A/D or digital input pin goes slightly negative, but R9 protects the MCU from damage here. If you use a MCU running on 3.3V, then use a 2.7V zener diode for D3.
*) Most small(?) ultrasound transducers operate around 40 KHz, so a gain of 13 (12) per stage is about as much as one can hope for from an inexpensive opamp like the TL082. This if you want something resembling a square wave on the output. Don't use a stone age opamp like the 741, it won't have enough gain to work here.
*) C4 and R5 forms a high pass filter, which limits low frequency gain below about 1.5 KHz. This helps reduce noise picked up from the mains, along with coping with other potential problems, as you string more gain stages together.
*) C5 and C6 are kind of optional but recommended, and again they are there to reduce the chance of running into problems as you add more gain. You may not get a perfect square wave on the output when using them, though that is probably not a problem for the MCU.
*) The total bandwidth for the whole amplifier would end up being about 2 to 100 KHz, more or less.
*) Depending on how you might build this, then I would recommend using a pair of TL082 chips, instead of using for instance a single TL084. This would allow you to put a bit of distance between the gain blocks, further reducing the risk of instability problems. Each chip should of course have its own pair of 0.1 uF decoupling caps right next to it.
*) I would start building one stage at a time, starting from the output and working my way back, and test each stage before proceeding. Would require some form of signal generator plus a scope to check, though.
*) You only wish to build this, if you truly don't care about the amplitude of the input signal, as there is no way of recovering that information from this circuit.