  A detailed next-to-next-to-leading order (NNLO) QCD analysis is performed for
the experimental data of the CCFR collaboration for the $xF_3$ structure
function. Theoretical ambiguities of the results of our NNLO fits are estimated
by application of the Pad\'e resummation technique and variation of the
factorization and renormalization scales. The NNLO and N$^3$LO $\alpha_s(Q^2)$
$\bar{MS}$-matching conditions are used. In the process of the fits we are
taking into account of twist-4 $1/Q^2$-terms. We found that the amplitude of
the $x$-shape of the twist-4 factor is decreasing in NLO and NNLO, though some
remaining twist-4 structure seems to retain in NNLO in the case when
statistical uncertainties are taken into account. The question of the stability
of these results to the application of the [0/2] Pad\'e resummation technique
is considered. Our NNLO results for $\alpha_s(M_Z)$ values, extracted from the
CCFR $xF_3$ data, are $\alpha_s(M_Z)=0.118 \pm 0.002 (stat) \pm 0.005 (syst)\pm
0.003 (theory)$ provided the twist-4 contributions are fixed through the
infrared renormalon model and $\alpha_s(M_Z)=0.121^{+0.007}_{0.010}(stat)\pm
0.005 (syst) \pm 0.003 (theory)$ provided the twist-4 terms are considered as
free parameters.
