The paper presents a method for computing the ionospheric total electron content (TEC) using the combination of the phase and code measurements at the frequencies f1 and f2 of the global positioning system, and applies it to study the TEC variations and disturbances during the magnetic storm in March 2015 using GPS continuous data in the Southeast Asia region. The computation results show that the TEC values calculated by using the combination of phase and code measurements are less dispersed than the ones by using only the pseudo ranges. The magnetic storm whose the main phase was on the 17th March 2015, with the minimum value of the SYM/H index of -223 nT is the biggest during the 24th solar cycle. In the main phase, the crests of the equatorial ionization anomaly (EIA) expanded poleward with large increases of TEC amplitudes, that provides evidence of the penetration of the magnetospheric eastward electric field into the ionosphere and of the enhancement of the plasma fountain effect associated with the upward plasma drifts. In the first day of the recovery phase, due to the effect of the ionospheric disturbance dynamo, the amplitude of northern crest decreased an amount of about 25% with respect to an undisturbed day, and this crest moved equatorward a distance of about 11o, meanwhile the southern crest disappeared completely. In the main phase the ionospheric disturbances (scintillations) developed weakly, meanwhile in the first day of the recovery phase, they were inhibited nearly completely. During the storm time, in some days with low magnetic activity (Ap<~50 nT), the ionospheric disturbances in the local night-time were quite strong. The strong disturbance regions with ROTI > 0.5 concentrated near the crests of the EIA. The latitudinal-temporal TEC disturbance maps in these nights have been established. The morphology of these maps shows that the TEC disturbances are due to the medium-scale travelling ionospheric disturbances (MSTID) generated by acoustic-gravity waves in the northern crest region of the EIA after sunset moving equatorward with the velocity of about 210 m/s.