[math-fun] Disk polyomino puzzle

It's difficult to enumerate disk polyominoes, because it's hard to recognize them. To illustrate this, I present a modest puzzle. I will give a set of lattice points. Either find a circular disk that covers these lattice points and no others, or prove that no such disk exists. Here is the set. I am abbreviating (x,y) to the two-digit code xy. 01 02 03 04 11 12 13 14 20 21 22 23 24 25 31 32 33 34 35 42 43 44.