  The KiDS Strongly lensed QUAsar Detection project (KiDS-SQuaD) aims at
finding as many previously undiscovered gravitational lensed quasars as
possible in the Kilo Degree Survey. This is the second paper of this series
where we present a new, automatic object classification method based on machine
learning technique. The main goal of this paper is to build a catalogue of
bright extragalactic objects (galaxies and quasars), from the KiDS Data Release
4, with a minimum stellar contamination, preserving the completeness as much as
possible, to then apply morphological methods to select reliable
gravitationally lensed (GL) quasar candidates. After testing some of the most
used machine learning algorithms, decision trees based classifiers, we decided
to use CatBoost, that was specifically trained with the aim of creating a
sample of extragalactic sources as clean as possible from stars. We discuss the
input data, define the training sample for the classifier, give quantitative
estimates of its performances, and finally describe the validation results with
Gaia DR2, AllWISE, and GAMA catalogues. We have built and make available to the
scientific community the KiDS Bright EXtraGalactic Objects catalogue
(KiDS-BEXGO), specifically created to find gravitational lenses. This is made
of $\approx6$ millions of sources classified as quasars ($\approx 200\,000$)
and galaxies ($\approx 5.7$M), up to $r<22^m$. From this catalog we selected
'Multiplets': close pairs of quasars or galaxies surrounded by at least one
quasar, presenting the 12 most reliable gravitationally lensed quasar
candidates, to demonstrate the potential of the catalogue, which will be
further explored in a forthcoming paper. We compared our search to the previous
one, presented in the first paper from this series, showing that employing a
machine learning method decreases the stars-contaminators within the GL
candidates.
