I found hits on three surnames so far. One thing to keep in mind is that spellings often changed over time, for example the surname Strode evolved into Stroud. This spelling change is even more exaggerated when French names became Anglicized.
Another problem is who knows the surname of your twenty seven times Great Grandmother though the female line only. I don’t have a clue what countries all of my 27th generations back ancestors lived in. On the other hand going back 160 generations I’m probably related to my namesake, if only through my Jewish ancestors (my Finnish ancestors, not so much). My Irish ancestors are a possibility, especially from the Anglo-Norman-Irish side (de Burge - Burke).