A haloscope of the QUAX--$agamma$ experiment composed of an oxygen-free high thermal conductivity-Cu cavity inside an 8.1 T magnet and cooled to $sim200$ mK is put in operation for the search of galactic axion with mass $m_asimeq43~mutext{eV}$. The power emitted by the resonant cavity is amplified with a Josephson parametric amplifier whose noise fluctuations are at the standard quantum limit. With the data collected in about 1 h at the cavity frequency $ u_c=10.40176$ GHz, the experiment reaches the sensitivity necessary for the detection of galactic QCD-axion, setting the $90%$ confidence level limit to the axion-photon coupling $g_{agammagamma}<0.639times10^{-13}$ GeV$^{-1}$.
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