  The $\mathcal{N}=2$ Landau--Ginzburg description provides a strongly
interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field
theory. It is conjectured that one such example is given by the two-dimensional
$\mathcal{N}=2$ Wess--Zumino model. Recently, the conjectured correspondence
has been studied by using numerical techniques based on lattice field theory;
the scaling dimension and the central charge have been directly measured. We
study a single superfield with a cubic superpotential, and give an
extrapolation method to the continuum limit. Then, on the basis of a
supersymmetric-invariant numerical algorithm, we perform a precision
measurement of the scaling dimension through a finite-size scaling analysis.
