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)
}
}