Hi,
is this what you mean?
MinimalPolynomial[-64*Root[1485117014933504 - 63358257770528768*#1 + 175880452588961792*#1^2 +
3597580217985531904*#1^3 + 2886620541237067776*#1^4 - 7978677590095298560*#1^5 +
1641255166207721472*#1^6 + 186956041840230400*#1^7 - 19269086342770688*#1^8 -
1443410130894848*#1^9 + 46783245950976*#1^10 + 3483359772672*#1^11 +
6879722240*#1^12 - 865370112*#1^13 - 1757568*#1^14 + #1^16 & , 4, 0]
,x]
Best wishes,
Marco