Determining the location of $\gamma$-ray emission in blazar jets is a challenging task. Pinpointing the exact location of $\gamma$-ray production within a relativistic jet can place strong constraints on our understanding of high-energy astrophysics and astroparticle physics. We present a study of the radio- and $\gamma$-bright flat-spectrum radio quasar (FSRQ) 4C +01.28 (PKS B1055+018) in which we try to pinpoint the emission site of several prominent GeV flares. This source shows prominent high-amplitude broadband variability on time scales ranging from days to years. We combine high-resolution VLBI observations provided by the Boston University (BU) Blazar Monitoring Program and multi-band radio light curves over a period of around nine years. We can associate two bright and compact newly ejected jet components with bright flares observed by the Fermi/LAT $\gamma$-ray telescope and at various radio frequencies. A cross-correlation analysis reveals the radio light curves systematically lag behind the $\gamma$-rays. In combination with the jet kinematics as measured by the VLBA, we use these cross-correlations to constrain a model in which the flares become observable at a given frequency when a plasma component passes through the region at which the bulk energy dissipation takes place at that frequency. We derive a lower limit of the distance of the $\gamma$-ray emitting region in 4C +01.28 of several parsecs from the jet base, well beyond the expected extent of the broad-line region. This observational limit challenges blazar-emission models that rely on the broad-line region as a source of seed photons for inverse-Compton scattering.