GREP from multiFasta file and keep headers

Hi there,

I am new to coding, consider yourself warned 😀

I have a multifasta file with 3′ UTR sequences of variable length. I would like to extract a 6-mer sequence; AGTCTC with 20 nts upstream and 20 nts downstream (but not the rest of the sequence from that 3’UTR or that particular line, just these 20+6+20 nucleotides).
I know I can do that with Grep;

grep -   "....................AGTCTC...................." 3UTR.fa  > 3UTR2.fa

However, this doesn’t give me a new Fasta file with headers..
I know I can use the -B option but this give me all the lines from header to my sequence of interest.

Any suggestions are much appreciated!

Cheers,
Marie