The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1  1 10  1  1  1  0  1  1  6  1  1 12 10  1  0  1  6  1  1 12  1  1  1  1  0  1  1  1  1  1  1  2
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12  9  1 10  0  3  1  6  5  1 15 12  1  1  3  1  9  1 10 15  1  3  6  0  5  1 10 15  0  5  0 10  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  0  0  0  8  0  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  0  8  8  0  0  0  0  8  0  0  8  0  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  0  8  8  0  0  0  0  8  8  0  0  8  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0  0  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  0  8  0  0  8  8  8  8  0  0  0  8  0  0  0  8  8  8  0  8  8  0  0  0  8  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  0  8  8  8  0  8  8  8  8  8  8  8  0  8  8  0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  8
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0  8  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  8  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  8  0  8  0  8  0  8  8  8  8  8  0  0  8  8  0  0  0  8  0  8  0  8  8  8  0  8  8  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+104x^44+36x^45+162x^46+184x^47+883x^48+984x^49+2956x^50+2872x^51+6139x^52+4096x^53+6112x^54+2920x^55+3105x^56+1000x^57+724x^58+168x^59+199x^60+28x^61+30x^62+40x^64+21x^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 10.7 seconds.