  We study the functional codes $C_h(X)$ defined by G. Lachaud in $\lbrack 10
\rbrack$ where $X \subset {\mathbb{P}}^N$ is an algebraic projective variety of
degree $d$ and dimension $m$. When $X$ is a hermitian surface in $PG(3,q)$,
S{\o}rensen in \lbrack 15\rbrack, has conjectured for $h\le t$ (where $q=t^2$)
the following result : $$# X_{Z(f)}(\mathbb{F}_{q}) \le h(t^{3}+ t^{2}-t)+t+1$$
which should give the exact value of the minimum distance of the functional
code $C_h(X)$. In this paper we resolve the conjecture of S{\o}rensen in the
case of quadrics (i.e. $h=2$), we show the geometrical structure of the minimum
weight codewords and their number; we also estimate the second weight and the
geometrical structure of the codewords reaching this second weight
