  We construct a collection of families of higher Chow cycles of type $(2,1)$
on a 2-dimensional family of Kummer surfaces, and prove that for a very general
member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of
the higher Chow group. Construction of the cycles uses a finite group action on
the family, and the proof of their linear independence uses Picard-Fuchs
differential operators.
