The flat-spectrum radio quasar (FSRQ) 4C +01.28 is a bright and highly variable radio and gamma-ray emitter. We aim to pinpoint the location of the gamma-ray emitting region within its jet in order to derive strong constraints on gamma-ray emission models for blazar jets. We use radio and gamma-ray monitoring data obtained with the Atacama Large Millimeter/submillimeter Array (ALMA), the Owens Valley Radio Observatory (OVRO), the Submillimeter Array (SMA) and the Large Area Telescope on board the Fermi Gamma-ray Space Telescope (Fermi/LAT) to study the cross-correlation between gamma-ray and multi-frequency radio light curves. Moreover, we employ Very Long Baseline Array (VLBA) observations at 43GHz over a period of around nine years to study the parsec-scale jet kinematics of 4C +01.28. To pinpoint the location of the gamma-ray emitting region, we use a model in which outbursts shown in the gamma-ray and radio light curves are produced when moving jet components pass through the gamma-ray emitting and the radio core regions. We find two bright and compact newly ejected jet components that are likely associated with a high activity period visible in the Fermi/LAT gamma-ray and different radio light curves. The kinematic analysis of the VLBA observations leads to a maximum apparent jet speed of beta_app_=19+/-10 and an upper limit on the viewing angle of phi<4deg. Furthermore, we determine the power law indices that are characterizing the jet geometry, brightness temperature distribution and core shift to be l=0.974+/-0.098, s=-3.31+/-0.31 and kr=1.09+/-0.17, respectively, which are all in agreement with a conical jet in equipartition. A cross-correlation analysis shows that the radio light curves follow the gamma-ray light curve. We pinpoint the location of the gamma-ray emitting region with respect to the jet base to the range of 2.6pc<dgamma<20pc. Our derived observational limits places the location of gamma-ray production in 4C +01.28 beyond the expected extent of the broad-line region (BLR) and therefore challenges blazar-emission models that rely on inverse Compton up-scattering of seed photons from the BLR.