Proper imaging requires keeping track of phase information, so you measure the distances more precisely.
It appears you're using 40Khz ultrasound transducers, so the wavelength should be about 8mm. You might want to try using less phase shift of the beam to tighten up the volume you're sweeping, and do it slower.
Try suspending a hard solid round object from 3 threads, and see how that responds. It should give you an idea of the "impulse" response in 3 dimensions, and thus a clue as to how to de-convolve the data.