I found the solution - more or less.
Sadly it is hardcoded in src/Content.php.
If you want a custom fieltype wich stores array values you have to change the select case in function getValues to:
default:
if (is_array($this->values[$field])) {
$newvalue[$field] = json_encode($this->values[$field]);
}else{
$newvalue[$field] = $this->values[$field];
}
break;
And in setValues there is a $serializedFieldTypes = array(...) where you have to manual add your custom field type.
Sadly this is not practical for extentions. But I will update my github with my changed Content.php for people who want to have a look.
When I was searching for an solution I reviewed a lot of source code of bolt master branch at github. For version 2.3 the storage layer is completely rebuild and as it seems there will be no need for any changes than. So hopefully with version >=2.3 the extention will work out of the box.
Nevertheless getStorageType() just just affect database field type and bolt just accepts 'text' here.
Hope I can help some people by answering my own question.
Thanks
Tobi