As a general rule, employment in the state of Michigan is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true. This means you can be terminated with a "real" reason. It also means you can be terminated for violations you didn't sign off on.
The only way you would have any legal claim is if you could prove that you were fired because of your race. However, this generally requires more than simply the fact that you are the only minority. Indeed, if that were all you needed, then ANY employment action against you that you did not approve of would be actionable on grounds of race discrimination. It's your employer's motivation that matters, and you can't prove motivation simply by the fact that there are no other minorities. Motivation is typically proven by things such as derogatory comments about your race, racial jokes, patterns of more favorable treatment to employees of other races (i.e. did your employer fail to write up white employees for the same violations that you were written up for?) Ultimately, the question is whether you can convince a jury, using all facts circumstances and arguments available, that "but for" your race you would not have been fired.
If you believe that you have facts suggestive of race discrimination, your recourse would be to file a complaint with the Equal Employment Opportunity Commission. The EEOC will investigate and attempt to mediate a resolution with your employer. That not forthcoming, they will either file a lawsuit on your behalf or issue you a "right to sue" letter, which will enable you to sue in civil court with the assistance of an attorney. Again, though, if you do not believe you have evidence of race discrimination then I am afraid you would not have any recourse, despite the fact that your termination was clearly unfair and unfounded.
I hope that you find this information helpful. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
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