[mitko]

Thanks, that was a very helpful comment. I had to reason backwards from "in what situation I'm guaranteed a line", and then, how do I get there. I was able to get 4 lines with a few tries. Here's my base2048 encoded game

ஜɧࢩݥҬuళࡑ௨ټถݹƓقฐࡑ௧ʝÐݶԨքଈݪݫට༨ஈடΟໃʮzටఴঅ୦Ѯໃa௨৫ІܝԥചWђߝsลஈமϺບઞzජТஈߝકІݜҫඨƖݷಏقКחಎؾɑݛkЂϼ०తನլݢသ૫ØঐಳUಮщ౻ऊԀঙങఢVםષථϭŋɼԻహҵ

[altvali]

You had the right idea, but you can tweak it to get 6: ಞজໃݎฆঘໃݞഢsງڣ௨uІݮతටଘݸభඨƙђࢲҨະࡉɷƥȣKϡuЅਘௐքධݹࠒѻІݚݸටไऄமҔ༨ຣҫටถݹଗقຣऄϥןUਘ௨ටॾ୶Ɛටไࡉɶٴलݹસඪܔঅࢳ൳Uॿԫƥϼঔଗ෮ຜࡀƶ