  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 phase 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.
