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The standard model axion seesaw Higgs portal inflation (SMASH) model is a well motivated, self-contained description of particle physics over a range of energy scales that predicts axion dark matter particles to exist within the mass range of $50-200\,μ$eV. To scan these masses an axion haloscope under a strong constant magnetic field must operate between 12 to 48 GHz. The ORGAN experiment (situated in Perth, Australia) is a microwave cavity axion haloscope that aims to search the majority of the mass range predicted by the SMASH model. Here we present results of Phase 1a, the first experiment to scan and search for axions in the microwave Ku Band. Our initial scan sets a new limit on the coupling of axions to two photons of $g_{aγγ}\geq 3\times 10^{-12}\, \textrm{GeV}^{-1}$ over the mass range $63.2$ to $67.1~μ$eV with $95\%$ confidence. This result is the most sensitive to date in this mass range, sufficient to exclude the well motivated ALP (Axion Like Particle) cogenesis model for dark matter, which adds ALPs to the standard model in the early universe to simultaneously explain the observed baryon and dark matter densities. To attain this level of sensitivity we utilised a TM$_{010}$ cylindrical cavity resonator, scanned between 15.28 to 16.23 GHz through the utilisation of a tuning rod. Measurements were performed over a duration of 3.5 weeks with a $74\%$ duty cycle, with the resonator coupled to a low noise HEMT amplifier and placed inside a superconducting solenoidal electromagnet of 11.5 Tesla in magnetic field strength.