  Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called
weakly isometric, if there exists a mapping J:C1->C2, such that for any x,y
from C1 the equality d(x,y)=d holds if and only if d(J(x),J(y))=d. Obviously
two codes are weakly isometric if and only if the minimal distance graphs of
these codes are isomorphic. In this paper we prove that Preparata codes of
length n>=2^12 are weakly isometric if and only if these codes are equivalent.
The analogous result is obtained for punctured Preparata codes of length not
less than 2^10-1.
