Many centuries ago the ancient Arabs invented the game of the 28 Dominoes. I propose today this contiguous conditions puzzle. You could play on the 8x7 rectangle. You could use ancient tiles or Windows Paint. Below there are the rules.

The puzzle has solutions. I checked it. I ask you to find the solution which has the smallest perimeter, defined as the sum of peripheral heads.

We have demonstrated by the Gerard's Polyomino Solution Engine that the 5 solutions below are the only possible solutions without head-head conjunctions.

Cover this chessboard by the 28 Domino pieces, with these new rules (no joker!).
It isn't trivial.