  We construct a $6$ derivative holographic superconductor model in the
$4$-dimensional bulk spacetimes, in which the normal state describes a quantum
critical (QC) phase. The phase diagram $(\gamma_1,\hat{T}_c)$ and the
condensation as the function of temperature are worked out numerically. We
observe that with the decrease of the coupling parameter $\gamma_1$, the
critical temperature $\hat{T}_c$ decreases and the formation of charged scalar
hair becomes harder. We also calculate the optical conductivity. An appealing
characteristic is a wider extension of the superconducting energy gap,
comparing with that of $4$ derivative theory. It is expected that this
phenomena can be observed in the real materials of high temperature
superconductor. Also the Homes' law in our present models with $4$ and $6$
derivative corrections is explored. We find that in certain range of parameters
$\gamma$ and $\gamma_1$, the experimentally measured value of the universal
constant $C$ in Homes' law can be obtained.
