https://mathoverflow.net/questions/19783/countable-paracompactness-normality-and-locally-countable-open-covers see comments for a scan of the thesis where the space is written up It'll be an example to this search https://topology.pi-base.org/spaces?q=T_4+%2B+countably+paracompact+%2B+not+paracompact+%2B+paralindelof (as always, I prefer if someone reads the article before adding it, I didn't yet)