Consider the planar polynomial system \[ \begin{array}{l} \frac{{dx}}{{dt}}= y^3+\delta x, \\ \frac{{dy}}{{dt}} = -x^3(1+y)+\delta\mu+\delta^2 ax \end{array}\tag{1} \] depending on the real parameters \( a,\mu,\delta \), where \( \delta \) is small. The unperturbed system \( ( \delta=0 ) \) has a degenerate center at the origin (the Jacobian is the zero matrix). In system (1) the invariant line \(y=-1\) represents a homoclinic contour at infinity. The authors prove that the phenomenon of canard explosion occurs in system (1), that is, there is a critical parameter \( \mu =\mu_c(\delta) \) such that there is an exponentially small interval near \( \mu_c \) a mall limit cycle of (1) increases abruptly. The authors provide an approximation of \( \mu_c \) in the form \( \mu_c(\delta) = \mu_2\delta^2 + \mu_4 \delta^4 +O(\delta^6) \), where expressions are provided for \( \mu_2 \) and \( \mu_4 \).