  We consider a narrow magneto-dipole transition in the $^{169}$Tm atom at the
wavelength of $1.14\,\mu$m as a candidate for a 2D optical lattice clock.
Calculating dynamic polarizabilities of the two clock levels
$[\text{Xe}]4f^{13}6s^2 (J=7/2)$ and $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ in the
spectral range from $250\,$nm to $1200\,$nm, we suggest the "magic" wavelength
for the optical lattice at $807\,$nm. Frequency shifts due to black-body
radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole
interaction and other effects which can perturb the transition frequency are
calculated. The transition at $1.14\,\mu$m demonstrates low sensitivity to the
BBR shift corresponding to $8\times10^{-17}$ in fractional units at room
temperature which makes it an interesting candidate for high-performance
optical clocks. The total estimated frequency uncertainty is less than $5
\times 10^{-18}$ in fractional units. By direct excitation of the $1.14\,\mu$m
transition in Tm atoms loaded into an optical dipole trap, we set the lower
limit for the lifetime of the upper clock level $[\text{Xe}]4f^{13}6s^2
(J=5/2)$ of $112\,$ms which corresponds to a natural spectral linewidth
narrower than $1.4\,$Hz. The polarizability of the Tm ground state was measured
by the excitation of parametric resonances in the optical dipole trap at
$532\,$nm.
