The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  8  2  1  8  2  1  1  1 12  1  1  1  2  2  1  1  0  2  1  2  1  1  1  1  1  1  1  2  1  2  2
 0  2  0  6  4  6 12  2  8  6 12 14  0  2  4 10  2 14  0  0  2  6  2  6  2  2 14  8 12 10  2  8  8  6 10 14 14  6  2  2 10  2  2 10  6  0 12 14 12 10 14 10  6
 0  0 12  0  4  0  0  0  8  4  4  4  4  4  0  4  0 12  4  8  0  8  8  4  8 12 12  4  0 12  8  4  8 12 12  0  0 12 12  4  4  4 12  4  0  0  4  8  4  4  8  4 12
 0  0  0 12  0  0  0  4 12  4 12  8  4  8 12  4  8  0  4  4  0  8  4 12  4  0  0  8  0  4  8  4  4 12  4  4  4  4 12  0 12  0  0  4 12  8  0  0  8  4  0  4 12
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  8  0  8  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  0  8  8  8  8  0  8  0  0  8  0  8  0  0  8  8  0  8  8  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  0  8  0  8  8  8  8  8  8  0  8  8  0  0  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  0  0  8  0  0  8  8  0  8  0  8  8  8

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+179x^44+24x^45+484x^46+256x^47+1247x^48+672x^49+2990x^50+2432x^51+6436x^52+3472x^53+6366x^54+2432x^55+2999x^56+672x^57+1122x^58+256x^59+458x^60+24x^61+150x^62+62x^64+24x^66+6x^68+3x^72+1x^76

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 17.4 seconds.