  Magnetars have been proposed to be the origin of FRBs soon after its initial
discovery. The detection of the first Galactic FRB 20200428 from SGR 1935+2154
has made this hypothesis more convincing. In October 2020, this source was
supposed to be in an extremely active state again. We then carried out a
1.6-hours follow-up observation of SGR 1935+2154 using the new ultra-wideband
low (UWL) receiver of the Parkes 64\,m radio telescope covering a frequency
range of 704$-$4032 MHz. However, no convincing signal was detected in either
of our single pulse or periodicity searches. We obtained a limit on the flux
density of periodic signal of $\rm 3.6\,\mu Jy$ using the full 3.3GHz bandwidth
data sets, which is the strictest limit for that of SGR 1935+2154. Our full
bandwidth limit on the single pulses fluence is 35mJy ms, which is well below
the brightest single pulses detected by the FAST radio telescope just two
before our observation. Assuming that SGR 1935+2154 is active during our
observation, our results suggest that its radio bursts are either intrinsically
narrowband or show a steep spectrum.
