What makes specific combinations of genes create bodies in a certain way?
It is not which genes you have, but how they interact, that makes you different from others.
Genes code for proteins. Proteins interact with other proteins. Some are enzymes while others are structurals, parts of even bigger structures. If one of these proteins is affected, the entire structure it is part of changes. All these changes as well as the interactions between genes, proteins, chemicals inside the cell and the external enviroment determine the final phenotype of the organism.
The cell is like a factory. It buys raw material (provided by the genotype) and it assembles it (with the help of proteins) into the final product ( the phenotype).