I assume that the dreamer dreamt of composing a palindrome in a dream.
Many writers and poets do dream about writing, the style of writing, etc. All my life, I have associated with journalists, writers, reporters, not those who present news through their mouths but with their typewriters as I did for many years as an English language journalist and professional translator, and their pens writing Chinese as I did for many years as a Chinese journalist, news writer and editorial writer.
Dreaming of trying to compose a palindrome is a good dream. It indicates literary creativity and innovation as well as personal advancement, improvement and progress towards high literary skills. It also indicates self motivation and new realms of literary exploration, both of which are needed by writers, especially when they suffer from a writer’s block.