I guess I would first try something like this:
This doesn't use the MAX232 at all but drives the transducer directly from two of your MCU's GPIO pins.
R17 and C15 are part of the TL074 circuitry in the schematic I posted above.
The way it works is this:
- to send a chirp you configure the GPIO pins to be outputs and then toggle them at 40KHz to drive the transducer.
- to use the transducer as a receiver set GPIO B to an output with a LOW output and configure GPIO A as an input. The received signal will pass through the op-amp circuit via R17 and C15.
The emitted chirp won't be as strong as you can get with the MAX232 but you'll get something.