  In [9], the codewords of small weight in the dual code of the code of points
and lines of Q(4, q) are characterised. Inspired by this result, using
geometrical arguments, we characterise the codewords of small weight in the
dual code of the code of points and generators of Q+(5, q) and H(5, q2), and we
present lower bounds on the weight of the codewords in the dual of the code of
points and k-spaces of the classical polar spaces. Furthermore, we investigate
the codewords with the largest weights in these codes, where for q even and k
sufficiently small, we determine the maximum weight and characterise the
codewords of maximum weight. Moreover, we show that there exists an interval
such that for every even number w in this interval, there is a codeword in the
dual code of Q+(5, q), q even, with weight w and we show that there is an empty
interval in the weight distribution of the dual of the code of Q(4, q), q even.
To prove this, we show that a blocking set of Q(4, q), q even, of size q2 +1+r,
where 0 < r < (q +4)/6, contains an ovoid of Q(4, q), improving on [5, Theorem
9].
