The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+20x^41+105x^42+272x^43+404x^44+568x^45+655x^46+768x^47+1032x^48+1336x^49+1587x^50+1834x^51+2035x^52+2138x^53+2360x^54+2320x^55+2342x^56+2242x^57+2104x^58+2012x^59+1606x^60+1376x^61+1037x^62+792x^63+655x^64+454x^65+299x^66+160x^67+107x^68+52x^69+42x^70+30x^71+10x^72+4x^73+1x^74+2x^75+2x^77+2x^78+2x^79

The gray image is a code over GF(2) with n=110, k=15 and d=41.
This code was found by Heurico 1.10 in 41.8 seconds.