Here is some more background information for the post, there is a "triple" software package that is detailed in FIRST, SECOND and THIRD.
The FOURTH package is a standalone update.
FIRST
"Release": "MOI3_EU_SKMQB_R23802P",
"MuVersion": "0238",
"SupportedTrains": [
"*_?133*",
"*_?134*",
"*_?136*",
"*_?137*",
"*_?138*",
"*_?139*",
"*_?140*",
"*_?141*",
"*_?142*",
"*_?143*",
"*_?144*",
"*_?145*",
"*_?146*",
"*_?147*",
"*_?148*",
"*_?149*",
"*_?150*",
"*_?151*",
"*_?152*",
"*_?153*",
"*_?154*",
"*_?155*",
"*_?156*",
"*_?157*",
"*_?201*",
"*_?205*",
"*_?207*",
"*_?208*",
"*_?210*",
"*_?212*",
"*_?214*",
"*_?216*",
"*_?218*",
"*_?220*",
"*_?222*",
"*_?224*",
"*_?226*",
"*_?228*",
"*_?230*",
"*_?232*",
"*_?234*",
"*_?236*",
"*_?238*"
],
As you can read, this does support the 0156 version, and then should update you to 0238 at the end.
SECOND
"Release": "MOI3_EU_SKMQB_P26810P",
"MuVersion": "0268",
"SupportedTrains": [
"*_?238*",
"*_?240*",
"*_?242*",
"*_?243*",
"*_?244*",
"*_?245*",
"*_?246*",
"*_?249*",
"*_?251*",
"*_?252*",
"*_?254*",
"*_?256*",
"*_?257*",
"*_?260*",
"*_?262*",
"*_?264*",
"*_?266*",
"*_?268*"
],
THIRD
"Release": "MOI3_EU_SKMQB_P27800P",
"MuVersion": "0278",
"SupportedTrains": [
"*_?268*",
"*_?270*",
"*_?272*",
"*_?274*",
"*_?276*",
"*_?278*"
],
FOURTH
"Release": "MOI3_EU_SKMQB_P30603P",
"MuVersion": "0306",
"SupportedTrains": [
"*_?268*",
"*_?270*",
"*_?272*",
"*_?274*",
"*_?276*",
"*_?278*",
"*_?300*",
"*_?302*",
"*_?304*",
"*_?306*"
],
Technically you can skip the 3rd update, and go directly to the 4th one.