The generator matrix

1 0 0 0 0 0 0 1 1 1 2 0 0 2 2 2 1 1 1 0 1 1 2 0 0 1 1 1 0 1 1 1 1 1 1 2 1 2 1 1 1 2 1 0 0 1 2 1 1 0 0 1 1 0 2 1
0 1 0 0 0 0 0 0 0 0 0 1 2 1 1 0 1 3 2 2 0 3 1 1 2 1 3 1 1 1 3 1 0 0 1 0 1 2 0 3 0 2 2 1 1 2 1 1 0 1 0 2 1 1 1 0
0 0 1 0 0 0 0 0 0 0 0 0 1 3 3 2 3 1 3 0 1 2 0 2 1 1 2 0 1 3 1 2 1 2 0 2 1 1 3 2 3 0 3 1 3 3 3 0 0 0 0 2 1 0 0 1
0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 3 1 1 2 2 2 0 2 1 1 2 1 1 2 2 1 0 1 0 3 3 1 1 2 2 0 0 2 3 2 2 2 3 1 0 2
0 0 0 0 1 0 0 0 1 1 1 2 0 1 1 1 2 0 2 0 2 1 3 3 3 2 0 1 2 3 1 0 0 1 0 0 1 1 0 2 2 3 1 1 1 1 0 0 2 0 1 1 3 0 0 2
0 0 0 0 0 1 0 1 0 1 3 2 0 3 3 3 0 2 1 3 3 3 0 0 2 1 2 2 3 2 3 1 2 1 1 3 3 1 3 3 0 2 0 2 1 2 2 0 1 1 0 1 1 2 3 3
0 0 0 0 0 0 1 1 3 2 1 1 1 2 3 0 0 3 2 1 1 2 2 3 2 1 1 0 0 0 0 0 1 3 0 0 3 2 0 1 2 2 0 1 0 3 1 0 1 1 1 1 1 0 0 3
0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 0 0 2 0 2 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 0 2 2 0 2 2 2 0 2 2 0 0 0 0 0 2 2 2 0 2

generates a code of length 56 over Z4 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+82x^43+269x^44+372x^45+505x^46+720x^47+884x^48+1092x^49+1322x^50+1422x^51+1791x^52+1950x^53+2137x^54+2442x^55+2422x^56+2466x^57+2259x^58+2222x^59+1949x^60+1584x^61+1327x^62+1012x^63+807x^64+584x^65+420x^66+258x^67+165x^68+126x^69+87x^70+34x^71+30x^72+18x^73+7x^74+2x^76

The gray image is a code over GF(2) with n=112, k=15 and d=43.
This code was found by Heurico 1.10 in 44.1 seconds.