Many of the the polynomials in the Klueners-Malle database and also in my
[database with John Jones][1] come from families in the way you correctly
describe.  So you have "reverse engineered" the source family.

This particular source family is the first of two similar families
described in Section 13 my [Galois number fields with small root discriminant][2] with Jones.  Your m and our t are related by m=-81/16 t.  The generic
Galois group of this family is 17T8 = SL_2(16).4 and so for almost
all t the specialized Galois group will be 17T8.  Section 13 discusses
some details of the specialization process.  In particular, specializing
at t=-8 keeps the Galois group at 17T8 and has the unusually 
small discriminant 2^16 3^20 5^16.  


  [1]: http://arxiv.org/abs/1404.0266
  [2]: http://cda.morris.umn.edu/~roberts/dpr/Research_files/lowgrd.pdf