ClearAll[Heron]
Heron[a_, b_, c_] := With[{s = (a + b + c)/2}, Sqrt[s (s - a) (s - b) (s - c)]]
PrintTemporary[Dynamic[{a, b, c}]];
results = Reap[
    Do[
     If[a < b + c \[And] b < c + a \[And] c < a + b,
      If[GCD[a, b, c] == 1,
       If[IntegerQ[Heron[a, b, c]],
        Sow[<|"Sides" -> {a, b, c}, "Area" -> Heron[a, b, c],
          "Perimeter" -> a + b + c, "MaximumSide" -> Max[a, b, c]|>]
        ]
       ]
      ]
     ,
     {a, 1, 200},
     {b, a, 200},
     {c, b, 200}
     ]
    ][[2, 1]];
results = SortBy[results, {#["Area"] &, #["Perimeter"] &, #["MaximumSide"] &}];
results // Length
Take[results, 10] // Dataset
Select[results, #["Area"] == 210 &] // Dataset