The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+138x^45+237x^46+668x^47+749x^48+1348x^49+1890x^50+1950x^51+2566x^52+2014x^53+1810x^54+1350x^55+606x^56+498x^57+261x^58+180x^59+46x^60+26x^61+24x^62+10x^63+6x^65+1x^66+2x^67+2x^69+1x^70

The gray image is a code over GF(2) with n=416, k=14 and d=180.
This code was found by Heurico 1.16 in 4.53 seconds.