The Center of the Milky Way emits radiation through all the electromagnetic spectrum due to the presence of several astrophysical phenomena. Various scientifical questions remain unsolved in the picture that emerge from observations, the main one being the presence and activity of a supermassive black hole at the Galactic Center. Also in the X-ray band a strong diffuse emission is detected up to 22 keV, it has been suggested that its origin is linked to past high energy activity of the Galactic Center. The French SIGMA soft gamma ray telescope on board the Russian Granat satellite observed the Galactic Center (GC) for about 9 * 106 seconds from 1990 to the end of 1997. Its unique imaging capabilities coupled with the unprecedented exposure already allowed us to set preliminary constraints on the persistent high energy emission from Sgr A*. Here we present a new analysis of the complete set of observations of this region taking into account the possible presence of diffuse emission in the low energy channels. This allows us both to test current advection models of high energy emission from SgrA* and to investigate on past high energy activity.