  We numerically study a model of interacting spin-$1/2$ electrons with random
exchange coupling on a fully connected lattice. This model hosts a quantum
critical point separating two distinct metallic phases as a function of doping:
a Fermi liquid with a large Fermi surface volume and a low-doping phase with
local moments ordering into a spin-glass. We show that this quantum critical
point has non-Fermi liquid properties characterized by $T$-linear Planckian
behavior, $\omega/T$ scaling and slow spin dynamics of the Sachdev-Ye-Kitaev
(SYK) type. The $\omega/T$ scaling function associated with the electronic
self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark
of a `skewed' non Fermi liquid.
