  The results of the more detailed NNLO QCD analysis of the CCFR data for
$xF_3$ SF are presented. The factorization scale uncertainties are analysed.
The NNLO results for $alpha_s(M_Z)$ and twist-4 contributions are obtained.
Despite the fact that the amplitude of the $x$-shape of the twist-4 factor is
consequently decreasing at the NLO and NNLO, our new QCD analysis seems to
reveal the remaining twist-4 structure at the NNLO level. The definite N$^3$LO
uncertainties are fixed using the [0/2] Pad\'e resummation technique.
