You can find a working web socket application at Re: WebSocket Custom Port Setting
It does not support MQTT over WebSockets. It also does not support security, although you can setup a TLS context and call appropriate websocket_connect
ZentriOS is a complete connectivity operating system designed to unleash the power of WICED.
ZentriOS removes the complication of designing your file system, network connectivity, RTOS and so forth. Often it can reduce your development time by up to 18 months as it allows you to focus solely on your application without the need to develop and maintain all the lower layers. ZentriOS can run independently as a peripheral to a host microcontroller or it can be in the primary core with a secure and encrypted sandbox in which to run your own application.
ZentriOS is available to developers and module manufacturers as a way of getting to market quickly and of course, it runs on Broadcom hardware so interoperability testing is second to none.
For more information take a look at docs.zentri.com
With respect to your specific need, you may want to look at this link also: Cloud MQTT Demo