  The extended coset leader weight enumerator of the generalized Reed-Solomon
$[q + 1, q - 3, 5]_q$ code is computed. The computation is considered as a
question in finite geometry. For this we need the classification of the points,
lines and planes in the projective three space under projectivities that leave
the twisted cubic invariant. A line in three space determines a rational
function of degree at most three and vice versa. Furthermore the double point
scheme of a rational function is studied. The pencil of a true passant of the
twisted cubic, not in an osculation plane gives a curve of genus one as double
point scheme. With the Hasse-Weil bound on Fq-rational points we show that
there is a 3-plane containing the passant.
