The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+28x^39+103x^40+210x^41+318x^42+514x^43+792x^44+968x^45+1365x^46+1730x^47+2148x^48+2550x^49+3072x^50+3432x^51+3946x^52+4386x^53+4415x^54+4854x^55+4832x^56+4562x^57+4127x^58+3672x^59+3058x^60+2596x^61+2131x^62+1654x^63+1299x^64+922x^65+678x^66+440x^67+298x^68+162x^69+129x^70+54x^71+33x^72+28x^73+21x^74+6x^75+2x^76

The gray image is a code over GF(2) with n=110, k=16 and d=39.
This code was found by Heurico 1.10 in 471 seconds.