Kurtz, in the end, is a rather enigmatic character. This goes for his writing and his last words as well. Along with "the horror, the horror" his scrawled statement "exterminate all the brutes", Kurtz' character is terminally associated with a madness that stems from a seemingly complete moral dissolution.
Isolated in the jungle and left with only his vast ambition as a final vestige of his old ("civilized") way of thinking, Kurtz has gone from a man poised to educate the natives of the Congo region to one prepared to commit the greatest atrocities and wipe them out.
...loneliness and alienation have taken their greatest toll on Kurtz, who, cut off from all humanizing influence, has forfeited the restraints of reason and conscience and given free rein to his most base and brutal instincts.
As he falls into his final madness, Kurtz' vision of himself becomes more and more grand until he ends as a failed god, unable to construct a new morality, unable to save or conquer, and ultimately alone and stripped of any meaning.