Extending geodetic and astrometric Very Long Baseline Interferometry (VLBI) observations from traditional centimeter wavebands to millimeter wavebands offers numerous scientific potentials and benefits. However, it was considered quite challenging due to various factors, including the increased effects of atmospheric opacity and turbulence at millimeter wavelengths. Here, we present the results of the first geodetic-mode VLBI experiment, simultaneously observing 82 sources at 22/43/88/132 GHz (K/Q/W/D bands) using the Korean VLBI Network (KVN). We introduced the frequency phase transfer (FPT) method to geodetic VLBI analysis, an approach for calibrating atmospheric phase fluctuations at higher frequencies by transferring phase solutions from lower frequencies. With a 2 minute scan, FPT improved the signal-to-noise ratio of most fringes, some by over 100%, thereby enhancing the detection rate of weak sources at millimeter wavebands. Additionally, FPT reduced systematic errors in group delay and delay rate, with the weighted root mean squares (WRMS) of the postfitting residuals decreasing from 25.0 to 20.5 ps at the W band and from 39.3 to 27.6 ps at the D band. There were no notable differences observed in calibrating atmospheric phase fluctuations at the K band (WRMS = 12.4 ps) and Q band (WRMS = 11.8 ps). This experiment demonstrated that the millimeter waveband can be used for geodetic and astrometric applications with high precision.