Best way to determine horizontal plane ℤ³ that contains most vectors of given vector of vectrs

[hermann@stamm-wilbrandt.de]

I have a vector of vectors in ℤ³ (result of qfminim()) and want to 
determine the z coordinate with maximal vectors in that plane.

The good thing with PARI/GP is, that I most times get what I want 
somehow, like here:

    L=[v[3]|v<-S];
    C=[[l,#[v|v<-S,v[3]==l]]|l<-[vecmin(L)..vecmax(L)]];
    mx=vecsort(C,2)[#C][1];
    P=[(Q*v)~|v<-S,v[3]==mx];

But sorting and iteration over all possible vecmin..vecmax values looks 
not nice.
Is there a more intuitive way to set P to all vectors in plane with 
maximal vectors?

Regards,

Hermann.