Precision measurements of active and reactive components of in-plane microwave surface impedance were performed in single crystals of optimally doped Fe-based superconductor Ba(Fe1−xCox)2As2 (x =0.074, Tc = 23 K). Measurements in a millimeter wavelength range (Ka−band, 35 to 40 GHz) were performed using whispering gallery mode excitations in the ultrahigh quality factor quasi-optical sapphire disk resonator with YBa2Cu2O7 superconducting (Tc = 90 K) endplates. The temperature variation of the London penetration depth is best described by a power law function, ∆λ(T ) ∼ T n , n = 2.8, in a reasonable agreement with radio-frequency measurements on crystals of the same batch. This power-law dependence is characteristic of nodeless superconducting gap in the extended s-wave pairing scenario with a strong pairbreaking scattering. The quasiparticle conductivity of the samples, σ1(T ), gradually increases with the decrease of temperature, showing no increase below Tc, in a notable contrast with the behavior found in the cuprates. The temperature-dependent quasiparticle scattering rate was analyzed in a two-fluid model, assuming the validity of the Drude description of conductivity and generalized expression for the scattering rate. This analysis allows to estimate the range of the values of a residual surface resistance from 3 to 6 mΩ.