GRID-file: get max extent for all z-values above given value

I have a GRID-file with a quite large extent.
For an automatic workflow I need the maximum extent/bounding-box for all z-values that are over a certain range.
For example: Get the maximum extent for all z-values that are greater or equal than 0.05

Is there a possibility to do that with Python, GDAL or GMT-tools (generic mapping tools), so that it can run automatically?