We demonstrate an ultrahigh-sensitive plasmonic sensing of gas, employing a two-dimensional (2D) dielectric grating fabricated by laser interference lithography. The 2D grating was designed with the period of 500 nm and prepared in an AZ1505 photoresist layer on a gold film of 20 nm thickness deposited on a fused silica glass substrate. The surface plasmon resonance (SPR) in the Kretschmann configuration with spectral interrogation was utilized to measure the response of the sensor to vapors of aqueous solution of ethanol. Based on measurement of the gas refractive indices with the reference Au/Cr/SF10 sample, the resonance wavelength dependence was obtained. The SPR response of the structure in a spectral range of 1.68-1.85 µm with a sensitivity of 8200-111,000 nm/RIU was revealed. The sensor provides significantly higher sensitivity in comparison to conventional and grating-based SPR sensors.