  In this paper we present measurements performed with a Micromegas X-ray
detector setup. The detector is a prototype in the context of the BabyIAXO
helioscope, which is under construction to search for an emission of the
hypothetical axion particle from the sun. An important component of such a
helioscope is a low background X-ray detector with a high efficiency in the
1-10 keV energy range. The goal of the measurement was to study techniques for
background discrimination. In addition to common techniques we used a
multi-layer veto system designed to tag cosmogenic neutron background. Over an
effective time of 52 days, a background level of $8.6 \times
10^{-7}\,\text{counts keV}^{-1}\,\text{cm}^{-2} \, \text{s}^{-1}$ was reached
in a laboratory at above ground level. This is the lowest background level
achieved at surface level. In this paper we present the experimental setup,
show simulations of the neutron-induced background, and demonstrate the process
to identify background signals in the data. Finally, prospects to reach lower
background levels down to $10^{-7} \, \text{counts keV}^{-1} \, \text{cm}^{-2}
\, \text{s}^{-1}$ will be discussed.
