Get Maximum value per row of an embedded 2D array to create an embedded 1D column vector

The problem is to search for a name in matrix, and to return every occurrence per row.
Please see attachment

My solution is in error because when a name appears more than once in a row, it appears more than once in the results.
My solution involves creating an 'embedded' 4x5 matrix and listing it out using SMALL.
I need to reduce that embedded matrix to a 4x1 vector containing the maximum of each row of the matrix, then use SMALL on that vector.
Unfortunately, I do not seem to be able to do it, though I can do it on an ordinary (not embedded) matrix using a statement like
MAX(OFFSET($D$51:$G$54,ROW()-ROW($D$55),0,1,4)).
I cannot use OFFSET on the embedded matrix.

Very appreciative of any help from more experienced people!

I solved this myself, but I had to introduce another column to sort the original result ignoring blanks and duplicates.