The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^44+44x^45+180x^46+146x^47+388x^48+730x^49+583x^50+1658x^51+706x^52+1642x^53+582x^54+694x^55+374x^56+142x^57+162x^58+62x^59+15x^60+2x^61+18x^62+5x^64+5x^66+2x^68+4x^70+2x^74

The gray image is a code over GF(2) with n=416, k=13 and d=176.
This code was found by Heurico 1.16 in 1.17 seconds.