The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+62x^44+168x^45+262x^46+394x^47+485x^48+632x^49+763x^50+842x^51+923x^52+948x^53+975x^54+1044x^55+1145x^56+1174x^57+1121x^58+1072x^59+943x^60+798x^61+749x^62+530x^63+452x^64+398x^65+206x^66+142x^67+84x^68+38x^69+18x^70+8x^71+4x^73+2x^74+1x^96

The gray image is a code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.10 in 11.5 seconds.