The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+56x^43+164x^44+256x^45+412x^46+526x^47+596x^48+646x^49+744x^50+914x^51+1050x^52+1112x^53+1084x^54+1152x^55+1192x^56+1106x^57+1039x^58+998x^59+840x^60+710x^61+528x^62+376x^63+323x^64+224x^65+152x^66+72x^67+58x^68+42x^69+8x^70+2x^71+1x^90

The gray image is a code over GF(2) with n=110, k=14 and d=43.
This code was found by Heurico 1.10 in 11.1 seconds.