Hello and welcome.
Building a gradiometer is simple when the functional concept is understood. But the logging, interpretation and plotting of readings is a much more complex, task for computing, with many hours of sweat and tears in signal processing and programming.
Two identical zillion-turn coils in soft iron core, set apart a given distance and rigidly held respect to each other will be equally influenced by the earth magnetic field.
Being their signals equal, a differential/instrumentation amplifier shows no output.
Dragging the rigid pair of coils across terrain, one of the coils will be sensing minute different signal than the other due to being more near to a disturbance.
That is the signal the differential amplifier outputs. That is your data. Tied to the exact position of the reading; that is more data. Tied to the speed of travel, that is more data. Tied to the heading, that is more data. All those ingredients and more together can make the mapping.
Miguel