  We report the most accurate measurement of the position of the weak
quadrupole S(2) 2-0 line in D$_2$. The spectra were collected with a
frequency-stabilized cavity ring-down spectrometer (FS-CRDS) with an ultra-high
finesse optical cavity ($\mathcal{F}$ = 637 000) and operating in the
frequency-agile, rapid scanning spectroscopy (FARS) mode. Despite working in
the Doppler-limited regime, we reached 40 kHz of statistical uncertainty and
161 kHz of absolute accuracy, achieving the highest accuracy for homonuclear
isotopologues of molecular hydrogen. The accuracy of our measurement
corresponds to the fifth significant digit of the leading term in QED
correction. We observe 2.3$\sigma$ discrepancy with the recent theoretical
value.
