  We prove that any completely regular code with minimum eigenvalue in any
geometric graph G corresponds to a completely regular code in the clique graph
of G. Studying the interrelation of these codes, a complete characterization of
the completely regular codes in the Johnson graphs J(n,w) with covering radius
w-1 and strength 1 is obtained. In particular this result finishes a
characterization of the completely regular codes in the Johnson graphs J(n,3).
We also classify the completely regular codes of strength 1 in the Johnson
graphs J(n,4) with only one case for the eigenvalues left open.
