Scala, 120 bytes
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    readLine.inits.flatMap(_.tails).toList.groupBy(l=>l).filter(x=>x._2.length<2).map(_._1).groupBy(_.length).minBy(_._1)._2

I started off with 140 which at least already fits into a tweet.

    readLine                                 input
    .inits.flatMap(_.tails).toList           get all substrings of that string
    .groupBy(l=>l).filter(x=>x._2.length<2)  remove substrings that occur more than once
    .map(_._1).groupBy(_.length)             take the substring and group by length
    .minBy(_._1)._2                          take the list of shortest substrings