Printing to HP DesignJet 4000, no official or open source drivers?
There is not a supported driver from HP, only for the PostScript model.

I have had the same issue in the past with a non-PS LaserJet 5, and I now use the 'Generic PCL driver' for mine.

The Gutenprint drivers currently do not have a version for your printer, although you may find some success using a similar model with a driver.