The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+47x^40+130x^41+283x^42+490x^43+766x^44+948x^45+1270x^46+1574x^47+2127x^48+2566x^49+3077x^50+3610x^51+3889x^52+4542x^53+4663x^54+4856x^55+4954x^56+4624x^57+4272x^58+3862x^59+3197x^60+2556x^61+2032x^62+1594x^63+1230x^64+842x^65+557x^66+354x^67+251x^68+162x^69+83x^70+40x^71+49x^72+14x^73+19x^74+4x^75+1x^76

The gray image is a code over GF(2) with n=110, k=16 and d=40.
This code was found by Heurico 1.10 in 460 seconds.