The SR04 transducer is tuned to 40Khz, the receiver of the module is tuned to 38Khz. For better accuracy the sr04 can be modified to receive on 40Khz; research required on your part at this point.
Anyways fixing the sr04 receiver will increase sensitivity.
The sr04 has a terrible higher voltage regulator for the transducer. Rebuilding the transducer regulator will be of great benefit.