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Drainage for earthen floored shed

I have an earthen floor shed (~12ft x 14ft) which is prone to flooding in heavy rain due to being built into a bank (see attached picture for the height of the surrounding retaining walls). There exists some external drainage (a covered french drain) as well as a shale internal drain, however, this fails to work in the heavier rain. The shed is currently used as a stable and the floor is matted. I'm not too sure what might work here but would like a drainage system constructed. The easiest way might be a closed drain straight across the driveway to the garden (~12m)? Happy to discuss further and provide additional pictures.