The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  4  1  2  1  1  0  1  1  1  4  0  4  1  4  1  2  1  1  2  1  4  0  2  2  2  1
 0 12  0  4  0  0  4 12  0  8  4  0  4  8  4  4  0  8  0  4 12  0  4  8 12  0  4 12 12 12  4  0 12 12  4  0  8  4 12  4 12 12  0 12  4  0 12 12  8  4  4  8 12  0  0
 0  0 12  4  0 12  4  0  0  4  0  8 12 12  8  4  8  4  4  4  0  8  4  8  0 12  4 12  8  8 12 12  4  0  8  4  0  8  8  8  8  4 12  8 12  4  4 12  4  4  8  4  0  0  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  0  0  8  8  0  8  0  8  8  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  0  8  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  0  0  8  0  8  0  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  8  8  0  0  0  0  8  0  8  8  0  8  8  0  8  0  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  8  8  0  0  0  8  8  0  8  0  8  8  0  8  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  8  0  8  8  8  8  8  0  0  0  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  8  8  0  8  8  0  8  0  8  8  8  0  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  0  0  8  8  0  8  0  0

generates a code of length 55 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+42x^44+54x^45+121x^46+128x^47+181x^48+274x^49+391x^50+726x^51+1168x^52+1736x^53+2214x^54+2362x^55+2215x^56+1740x^57+1158x^58+732x^59+378x^60+254x^61+153x^62+132x^63+78x^64+34x^65+47x^66+14x^67+24x^68+4x^69+8x^70+2x^71+5x^72+4x^74+4x^76

The gray image is a code over GF(2) with n=440, k=14 and d=176.
This code was found by Heurico 1.16 in 6.05 seconds.