your code is 99% complete. only one thing is left.
if you are using bootstrap (i believe it is) then after putting HTML in you container div you have to invoke .modal method.
success: function (result) {
$('#modalMarkup').html(result);
$('#modalMarkup').modal('show');
}
If above code doesnot work then try to put the #modalMarkup html in Moda-body container not in the parent div.