One possibility would be to synthesize polyamide 6 (from caprolactam), in the presence of a MWCNT dispersion. In this way, it is to be expected that the dispersion of the nanotubes would be good enough.
Dispersing carbon nanotubes, especially in a polymer, is complicated because homogeneous mixtures are not generated. The alternative is to prepare the polymer in a suspension of nanotubes. In this way, the degree of dispersion of the nanotubes in the material (once polymerized) will be much greater.
You can see this paper that I include in the message. In this case, it is montmorillonite (and not MWNTs) but to get an idea of the procedure I think it may be useful...
It is very difficult to homogeneously disperse nano-particles in polymer. There are various methods to fabricate the nano-composite. You can refer this article to get an overview of the methods.