The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+134x^44+100x^45+451x^46+632x^47+1497x^48+2424x^49+3590x^50+5040x^51+5043x^52+5032x^53+3737x^54+2424x^55+1377x^56+632x^57+346x^58+96x^59+118x^60+4x^61+59x^62+20x^64+8x^66+1x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 10.7 seconds.