  The weight distribution of the binary self-dual $[128,64]$ code being the
extended code $C^{*}$ of the code $C$ spanned by the incidence vectors of the
blocks of the polarity design in $PG(6,2)$ [11] is computed. It is shown also
that $R(3,7)$ and $C^{*}$ have no self-dual $[128,64,d]$ neighbor with $d \in
\{ 20, 24 \}$.
