The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  4  1  1  1  1 10 12  1  1  2  1  1  1  1  1  0  1  6 14  1  1  8  1  1 10  1  1 14  4  1  2 12 14 12  1  4  2  8  8  1  1  1  1
 0  1 11 14  5  1  0  3  1  6  1 13  1  4 15 10  1  1  1 12  9  1  2  7 11  5  3  1 15  1  1 14  8  1  6  7  1 14 13  1  2  4  1  1  1  1 15  1  1  2  2  4  3  3  0
 0  0 12  4  0  4 12  0  0  8 12 12  4  4  8  0 12  0  0  8  8  4 12 12 12  0  8  8  8  0  4  4  4  4  8 12  8  4  4  4  4 12 12  8  4  8  8  4 12 12  4 12  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  0  8  0  8  0  0  8  8  0  8  0  0  8  0  8  0  0  0  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  8  8  0  8  8  8  0  8  8  0  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  8  0  8  0  8  8  0  8  8  0  8  0  8  0  0  8  8  8  8  8  8  0  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  0  0  8  8  0  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+25x^44+48x^45+125x^46+240x^47+340x^48+832x^49+1309x^50+2982x^51+4492x^52+7790x^53+9093x^54+10972x^55+9103x^56+7892x^57+4464x^58+2984x^59+1295x^60+800x^61+315x^62+212x^63+74x^64+44x^65+41x^66+18x^67+18x^68+2x^69+11x^70+9x^72+2x^74+2x^76+1x^80

The gray image is a code over GF(2) with n=440, k=16 and d=176.
This code was found by Heurico 1.16 in 40.2 seconds.