The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+70x^45+168x^46+186x^47+469x^48+544x^49+1112x^50+994x^51+1166x^52+1042x^53+1122x^54+498x^55+369x^56+170x^57+134x^58+46x^59+34x^60+24x^61+22x^62+4x^63+8x^64+6x^65+2x^66+1x^72

The gray image is a code over GF(2) with n=416, k=13 and d=180.
This code was found by Heurico 1.16 in 56.2 seconds.