  With the purpose to investigate the radio emission of new ultracool objects,
we carried out a targeted search in the recently discovered system VHS
J125601.92$-$125723.9 (hereafter VHS 1256$-$1257); this system is composed by
an equal-mass M7.5 binary and a L7 low-mass substellar object located at only
15.8\,pc. We observed in phase-reference mode the system VHS 1256$-$1257 with
the Karl G. Jansky Very Large Array at $X$- and $L$- band and with the European
VLBI Network at $L$-band in several epochs during 2015 and 2016. We discovered
radio emission at $X$-band spatially coincident with the equal-mass M7.5 binary
with a flux density of 60 $\mu$Jy. We determined a spectral index $\alpha =
-1.1 \pm 0.3$ between 8 and 12 GHz, suggesting that non-thermal,
optically-thin, synchrotron or gyrosynchrotron radiation is responsible for the
observed radio emission. Interestingly, no signal is seen at $L$-band where we
set a 3-$\sigma$ upper limit of 20 $\mu$Jy. This might be explained by strong
variability of the binary or self-absorption at this frequency. By adopting the
latter scenario and gyrosynchrotron radiation, we constrain the turnover
frequency to be in the interval 5--8.5 GHz, from which we infer the presence of
kG-intense magnetic fields in the M7.5 binary. Our data impose a 3-$\sigma$
upper bound to the radio flux density of the L7 object of 9 $\mu$Jy at 10\,GHz.
