There is an option in the MySQLi recordset parameter that will allow you to pass parameters as "comma separated list". This will allow you to use an IN statement in your query to allow multiple selections like:
SELECT * FROM Table WHERE postalCode IN (param)
then param can be set to allow comma separated lists and then you name all your checkboxes with the same name (with brackets so they are passed as an array) like: name="postalCheck"
Then set the parameter value to create a comma separated list from the array like: <?php echo(implode(",",$_POST['postalCheck'])); ?>