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We present an optical transmission spectrum for WASP-94A b, the first atmospheric characterisation of this highly-inflated hot Jupiter. The planet has a reported radius of $1.72^{+0.06}_{-0.05}$ R$_{\textrm{Jup}}$, a mass of only $0.456^{+0.032}_{-0.036}$ M$_{\textrm{Jup}}$, and an equilibrium temperature of $1508 \pm 75$ K. We observed the planet transit spectroscopically with the EFOSC2 instrument on the ESO New Technology Telescope (NTT) at La Silla, Chile: the first use of NTT/EFOSC2 for transmission spectroscopy. We achieved an average transit-depth precision of $128$ ppm for bin widths of $\sim200$ Angstrom. This high precision was achieved in part by linking Gaussian Process hyperparameters across all wavelength bins. The resulting transmission spectrum, spanning a wavelength range of $3800 - 7140$ Angstrom, exhibits a sodium absorption with a significance of $4.9σ$, suggesting a relatively cloud-free atmosphere. The sodium signal may be broadened, with a best fitting width of $78_{-32}^{+67}$ Angstrom in contrast to the instrumental resolution of $27.2 \pm 0.2$ Angstrom. We also detect a steep slope in the blue end of the transmission spectrum, indicating the presence of Rayleigh scattering in the atmosphere of WASP-94A b. Retrieval models show evidence for the observed slope to be super-Rayleigh and potential causes are discussed. Finally, we find narrow absorption cores in the CaII H&K lines of WASP-94A, suggesting the star is enshrouded in gas escaping the hot Jupiter.