¿Cómo hacer un UIPickerView con un botón Listo?

Tengo dificultades para hacer que aparezca un UIPickerView con un botón listo cuando los usuarios tocan un UITextField. Este es mi código hasta ahora. Todo funciona bien, pero cuando toco el campo de texto, aparece el teclado, no el selector.

class ViewController: UIViewController, UIPickerViewDataSource, UIPickerViewDelegate {


@IBOutlet var textField1: UITextField!

let pickerData = ["11", "12", "13"]





@IBAction func textButton(sender: AnyObject) {

    let picker: UIPickerView
    picker = UIPickerView(frame: CGRectMake(0, 200, view.frame.width, 300))
    picker.backgroundColor = .whiteColor()

    picker.showsSelectionIndicator = true
    picker.delegate = self
    picker.dataSource = self

    let toolBar = UIToolbar()
    toolBar.barStyle = UIBarStyle.Default
    toolBar.translucent = true
    toolBar.tintColor = UIColor(red: 76/255, green: 217/255, blue: 100/255, alpha: 1)
    toolBar.sizeToFit()

    let doneButton = UIBarButtonItem(title: "Done", style: UIBarButtonItemStyle.Plain, target: self, action: "donePicker")
    let spaceButton = UIBarButtonItem(barButtonSystemItem: UIBarButtonSystemItem.FlexibleSpace, target: nil, action: nil)
    let cancelButton = UIBarButtonItem(title: "Cancel", style: UIBarButtonItemStyle.Plain, target: self, action: "donePicker")

    toolBar.setItems([cancelButton, spaceButton, doneButton], animated: false)
    toolBar.userInteractionEnabled = true

    textField1.inputView = picker
    textField1.inputAccessoryView = toolBar




}



override func viewDidLoad() {
    super.viewDidLoad()
    // Do any additional setup after loading the view, typically from a nib.
}

override func didReceiveMemoryWarning() {
    super.didReceiveMemoryWarning()
    // Dispose of any resources that can be recreated.
}

func numberOfComponentsInPickerView(pickerView: UIPickerView) -> Int {
    return 1
}

func pickerView(pickerView: UIPickerView, numberOfRowsInComponent component: Int) -> Int {
    return pickerData.count
}

func pickerView(pickerView: UIPickerView, titleForRow row: Int, forComponent component: Int) -> String? {
    return pickerData[row]
}

func pickerView(pickerView: UIPickerView, didSelectRow row: Int, inComponent component: Int) {
    textField1.text = pickerData[row]
}

func donePicker() {

    textField1.resignFirstResponder()

}




}

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