It would be extremely difficult to expunge a DWI conviction. One could spend many, many thousands of dollars in the attempt, which would be unliklely to be successful, for several reasons. The Minnesota Department of Public Safety regulates drivers licenses, under authority of state statute and administrative rules. You could ask them what the legal; basis for their requirement is. There is not enough information presented here to venture a guess.
For all intents and purposes, a DWI cannot be expunged. Even if a court was inclined to expunge the criminal DWI charge (which is not likely) , the civil revocation would still appear on the administrative record and be viewed as a DWI.
Your question actually raises to possible issues.
The first is more directly related to your question of whether a DWI conviction can be removed from your driving record.
The Minnesota DWI Statutes have an enhancement provision related to any DWI related license revocation or criminal conviction. In these instances, there is a ten year look-back period.
Many years ago there was a provision permitting removing of a DWI from your driving record. However, even with that provision, the State never granted the request.
They closed this provision when they revised the DWI statute over ten years ago and there is simply no administrative or procedural way to redact your driving record.
This raisws the the second possible issue - expungement. Expungement is when you request that all records pertaining to your DWI be sealed. This would include your court file, your record with the Bureau of Criminal Apprehension, the Prosecuting Attorney, the Probation Department and Driver and Vehicle Services.
This is even more difficult than simply trying to remove a DWI froom your driving record.
As previously mentioned, there is a ten year look-back period for DWI enhancement. Therefore, in theory, since your offense occurred some 25 years ago, the enhancement provisions do not apply to you as the law stands in 2011 and it would seem possible to present a convincing argument that you are disproportionately disadvantaged by having a DWI on your record.
However, the look-back period has changed several times since your 1986 offense took place.
First there was no look-back period, and all DWI's were trated as Misdemeanors. Then they began a five year look-back period to charge gross misdemeanor offenses. More recently they changed it to a ten year look back period and added a potential felony DWI charge.
It seems likely that we should antcipate the eventual lifetime look-back period, and therefore expungement will become a legal impossibility rather than simply an improbability.
Simply put the issue is too politically charged for anyone to agree to expunge a DWI or remove one from your driving record.
You therefore can file the expungement petition, however the result is likely a foregone conclusion.