Pay attention to details and efficiency. Check for errors. You asked for files so skip directories and other things. Allow for multiple files with the same modified time stamp (for example, Windows file times have a resolution of, at best, 100-nanoseconds). You already have ModTime() so don't call os.Stat(). Use time.Time methods directly. And so on.

For example,

package main

import (
    "fmt"
    "io/ioutil"
    "os"
    "time"
)

func main() {
    dir := `C:\temp\` // Windows directory
    files, err := ioutil.ReadDir(dir)
    if err != nil {
        fmt.Fprintln(os.Stderr, err)
        os.Exit(1)
    }
    var modTime time.Time
    var names []string
    for _, fi := range files {
        if fi.Mode().IsRegular() {
            if !fi.ModTime().Before(modTime) {
                if fi.ModTime().After(modTime) {
                    modTime = fi.ModTime()
                    names = names[:0]
                }
                names = append(names, fi.Name())
            }
        }
    }
    if len(names) > 0 {
        fmt.Println(modTime, names)
    }
}