  We have investigated the low temperature specific heat properties as a
function of magnetic field in the strongly correlated layered cobalt oxide
[BiBa$_{0.66}$K$_{0.36}$O$_2$]CoO$_2$. These measurements reveal two kinds of
magnetic field dependent contributions in qualitative agreement with the
presence of a previously inferred magnetic Quantum Critical Point (QCP). First,
the coefficient of the low temperature T$^3$ behavior of the specific heat
turns out to sizeably decrease near a magnetic field consistent with the
critical value reported in a recent paper. In addition, a moderate but
significant enhancement of the Sommerfeld coefficient is found in the vicinity
of the QCP suggesting a slight increase of the electronic effective mass. This
result contrasts with the divergent behavior of the previously reported Pauli
susceptibility. Thus, a strongly enhanced Wilson ratio is deduced, suggesting
efficient ferromagnetic fluctuations in the Fermi liquid regime which could
explain the unusual magnetic field dependent specific heat. As a strong check,
the high magnetic field Wilson ratio asymptotically recovers the universal
limit of the local Fermi liquid against ferromagnetism.
