When z = 1, the only solutions are (9,44) and (44,9)

When z = 2, the only solutions are (18,88) and (88,18)

When z = 3, the only solutions are (27,132) and (132,27)

When z = 4, the only solutions are (36,176) and (176,36)

When z = 5, the solutions are (45,220),(96,203),(149,168), and their "reverses".

So, the 4 smallest solutions are (9,44), (44,9), (18,88) and (88,18).

The 4 smallest distinct values of X + Y are 53, 106, 153, and 212