Use PuTTY behind a Proxy

This is most likely not the answer you want, but if your network admin has correctly configured the proxy, then you can't connect through it.

I am guessing they don't want to allow non-http(s) traffic, so there won't be much you can do about it. You could try running your ssh server on port 80 or port 443 and see if they allow you to connect to it that way.