Может так?
$news = self::find()
->where(['status' => self::STATUS_ENABLE, 'datePublished' => '<2016-04-04'])->all();
или так -
$news = self::find()
->where(['status' => self::STATUS_ENABLE'])->andWhere('datePublished < :datePublished',[':datePublished' => '2016-04-04'])->all();