I Googled "minnesota gis data", which took me to the Minnesota Geographic Data Clearinghose.
From there I selected Data, then under Data Catalogs, I selected Mn/DOT (i.e. Department of Transportation).
At the next webspace, under the GIS maps heading (right side, half-way down), I selected "MnDOT basemap data files".
Here, needing some additional reference info, I followed the Statewide Data link and downloaded the MN State Boundary, MN County Boundaries, Trunk Highway System (?), and Municipal Boundaries.
Next, I created a shapefile of your region of interest (RIO) using the Well Known Text (WKT) expression for your bounding box coordinates. The goal was to determine which county your ROI fell within (because the MnDOT high definition road data is split apart by county). That said, the WKT expression for your RIO is this:
POLYGON ((-93.28587 44.9674, -93.28587 44.9855, -93.25351 44.9855, -93.25351 44.9674, -93.28587 44.9674))
Finally, as you see in this screenshot, I was able to determine that your ROI fell in Hennepin County, Minnesota:
- Dark Green = State Background
- Light Green = Hennepin County
- Orange Boundary = Minneapolis (visualized for convenience)
- Yellow Boundary = your ROI.
Once I knew I needed the Hennepin County MnDOT data, I returned to the MnDOT basemap data files site mentioned earlier, selected County Based, then chose Hennepin County.
Do this, and you'll find a lonesome dataset just waiting for you. Or in other words, this exact file.
Having said all this, all I really did was follow the advice of @wstewart1958 and apply some GIS basics (admittedly the WKT stuff was probably over the top, but all you needed was a 4-point polygon defining your ROI to visualize the placement).