This is an interesting question for two reasons: Traditionally, Hemingway's heroes are male, and many reviewers interpret Catherine as an undeveloped character in the novel, merely an idealized projection of male desire. Upon closer examination, however, Catherine does share characteristics of the code hero.
Hemingway's code hero is a skilled professional; Catherine is a nurse who is skilled in her profession. The code hero lives with courage in a dangerous world; Catherine demonstrates courage when she and Frederic row across the lake to escape into Switzerland, a very dangerous feat, and especially when she tries to deliver their baby, finally realizing that she will die. The code hero lives in a random universe, but chooses to control himself and endure; Catherine cannot control events when she goes into labor, but she endures the pain with dignity until her death.
Catherine endures in other ways, as well. She experiences the death of a fiance, faces great fear as an unmarried nurse when she learns she is pregnant, and suffers enormously when Frederic leaves her to return to the war. Throughout all of these trials, however, Catherine does not feel sorry for herself, and she does not break. Like a code hero, she endures.