The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+87x^40+408x^42+1040x^44+2128x^46+3395x^48+5120x^50+7104x^52+8650x^54+9399x^56+8750x^58+7350x^60+5316x^62+3461x^64+1844x^66+896x^68+378x^70+144x^72+38x^74+18x^76+8x^78+1x^80

The gray image is a code over GF(2) with n=112, k=16 and d=40.
This code was found by Heurico 1.10 in 167 seconds.