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The current flag dates back to the middle ages, maybe as far as the 12th century. This makes it not only one of the youngest national flags of the world (since 2004), but also one of the oldest! (Even if it has been in disuse for most of its history.)
The red cross on white background comes from the flag of the late antique Kingdom of Iberia (located in present day Georgia and unrelated to the Iberian Peninsula). The four crosses are Bolnisi crosses, a Georgian national symbol, taken from an ornament found in the 5th century Bolnisi Sioni church.
Also check out their quite different naval ensign:
that's dark red to me not brown