A quick Google search yields over a million and a half hits for injustice

'unjustice' is an incorrect extension of 'unjust'

I would probably never use the word 'unjustice' - it just doesn't sound as natural to me as 'injustice' - both both are actually in the dictionary:

"Source: Webster's Revised Unabridged Dictionary (1913)

Unjustice \Un*jus"tice\, n.
Want of justice; injustice. [Obs.] --Hales."

"Injustice \In*jus"tice\, n. [F. injustice, L. injustitia. See
In- not, and Justice, and cf. Unjust.]
1. Want of justice and equity; violation of the rights of
another or others; iniquity; wrong; unfairness;
imposition.

If this people [the Athenians] resembled Nero in
their extravagance, much more did they resemble and
even exceed him in cruelty and injustice. --Burke.

2. An unjust act or deed; a sin; a crime; a wrong.

Cunning men can be guilty of a thousand injustices
without being discovered, or at least without being
punished. --Swift."
http://dict.die.net