Filtering solutions in PowerRepresentations

I have the following code:

PowersRepresentations[10400, 7, 2]

This produces Length[PowersRepresentations[10400, 7, 2]]=433789 number of solutions. Now I want to filter in those solutions, the filter must remove the solutions when it does not exist of distinct integers (so for example $left{35, 35, 35, 36, 38, 41, 48right}$ must be removed because the number $35$ is used three times) and all the integers must be bigger than zero (so for example $left{0, 0, 0, 0, 0, 20, 100right}$ must be removed because the number $0$ is used and it is used five times). How do I code that?