The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+44x^41+149x^42+316x^43+507x^44+714x^45+1040x^46+1336x^47+1644x^48+2044x^49+2485x^50+3034x^51+3545x^52+4116x^53+4413x^54+4616x^55+4914x^56+4858x^57+4563x^58+4246x^59+3748x^60+3102x^61+2677x^62+2138x^63+1633x^64+1224x^65+847x^66+574x^67+349x^68+256x^69+180x^70+116x^71+38x^72+22x^73+28x^74+6x^75+3x^76+4x^77+1x^78+2x^79+2x^80+1x^86

The gray image is a code over GF(2) with n=112, k=16 and d=41.
This code was found by Heurico 1.10 in 362 seconds.