We present an anisotropic analysis of baryon acoustic oscillation (BAO) signal from the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. The sample consists of 147 000 quasars distributed over a redshift range of 0.8 < z < 2.2. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement DM at z = 2.2 and Hubble parameter H at z = 0.8. We parametrize the distance-redshift relation, relative to a fiducial model, as a Taylor series. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine DM(z = 1) = 3405 ± 305 (rd/rd, fid)Mpc, H(z = 1) = 120.7 ± 7.3 (rd, fid/rd) kms-1 Mpc-1 andDM(z=2)=5325±249 (rd/rd, fid)Mpc, H(z = 2) = 189.9 ± 32.9 (rd, fid/rd) km s-1 Mpc-1. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.