Objects are three bit binary numbers. Morphisms exists when you can flip some bits from 1 to 0 (but not the other way around).

digraph G {

"000";
"001";
"010";
"011";

"100";
"101";
"110";
"111";

"001" -> "000";
"010" -> "000";
"100" -> "000";

"011" -> "001";
"011" -> "010";

"111" -> "101";
"111" -> "110";
"111" -> "011";

"101" -> "100";
"101" -> "001";
"110" -> "100";
"110" -> "010";
}