We study the rotation of a $^{87}$Rb Bose-Einstein condensateconfined in a magnetic trap to which a focused, off resonantgaussian laser beam is superimposed. The confining potential iswell approximated by the sum of a quadratic and a quartic termwhich allows to increase the rotation frequency of the gas abovethe trap frequency. In this fast rotation regime we observe adramatic change in the appearance of the quantum gas. The vorticeswhich were easily detectable for a slower rotation become muchless visible, and their surface density is well below the valueexpected for this rotation frequency domain. We discuss somepossible tracks to account for this effect.