  We investigate the long GRB140629A through multiwavelength observations,
which cover optical, infrared and X-rays between 40s and 3yr after the burst,
to derive the properties of the dominant jet and its host galaxy. Polarisation
observations by the MASTER telescope indicate that this burst is weakly
polarised. The optical spectrum contains absorption features, from which we
confirm the redshift of the GRB as originating at z=2.276. We performed
spectral fitting of the X-rays to optical afterglow data and find there is no
strong spectral evolution. We determine the hydrogen column density to be
7.2x10^21cm^-2 along the line of sight. The afterglow in this burst can be
explained by a blast wave jet with a long-lasting central engine expanding into
a uniform medium in the slow cooling regime. At the end of energy injection, a
normal decay phase is observed in both the optical and X-ray bands. An
achromatic jet break is also found in the afterglow light curves 0.4d after
trigger. We fit the multiwavelength data simultaneously with a model based on a
numerical simulation and find that the observations can be explained by a
narrow uniform jet in a dense environment with an opening angle of 6.7deg
viewed 3.8deg off-axis, which released a total energy of 1.4x10^54erg. Using
the redshift and opening angle, we find GRB 140629A follows both the Ghirlanda
and Amati relations. From the peak time of the light curve, identified as the
onset of the forward shock (181s after trigger), the initial Lorentz factor is
constrained in the range 82-118. Fitting the host galaxy photometry, we find
the host to be a low mass, star-forming galaxy with a star formation rate of
logSFR=1.1^+0.9_-0.4Myr^-1. We obtain a value of the neutral hydrogen density
by fitting the optical spectrum, logN(HI)=21.0+-0.3, classifying this host as a
damped Lyman-alpha. High ionisation lines are also detected in the spectrum.
