  The extended environment of galaxies contains a wealth of information about
the formation and life cycle of galaxies which are regulated by accretion and
feedback processes. Observations of neutral hydrogen are routinely used to
image the high brightness disks of galaxies and to study their kinematics.
Deeper observations will give more insight into the distribution of diffuse gas
in the extended halo of the galaxies and the IGM, where numerical simulations
predict a cosmic web of extended structures and gaseous filaments. To observe
the extended environment of galaxies, column density sensitivities have to be
achieved that probe the regime of Lyman limit systems. HI observations are
typically limited to a brightness sensitivity of NHI~10^19 cm-2, but this must
be improved upon by ~2 orders of magnitude. In this paper we present the
interferometric data of the Westerbork Virgo HI Filament Survey (WVFS) - the
total power product of this survey has been published in an earlier paper. By
observing at extreme hour angles, a filled aperture is simulated of 300x25
meters in size, that has the typical collecting power and sensitivity of a
single dish telescope, but the well defined bandpass characteristics of an
interferometer. With the very good surface brightness sensitivity of the data,
we hope to make new HI detections of diffuse systems with moderate angular
resolution. The survey maps 135 degrees in Right Ascension between 8 and 17
hours and 11 degrees in Declination between -1 and 10 degrees, including the
galaxy filament connecting the Local Group with the Virgo Cluster. Only
positive declinations could be completely processed and analysed due to
projection effects. A typical flux sensitivity of 6 mJy beam-1 over 16 km s-1
is achieved, that corresponds to a brightness sensitivity of NHI~10^18 cm-2. In
total, 199 objects have been detected, of which 17 are new HI detections.
(Abridged)
