The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+72x^45+278x^46+474x^47+546x^48+1052x^49+1178x^50+1330x^51+1030x^52+926x^53+517x^54+286x^55+203x^56+136x^57+72x^58+70x^59+12x^60+6x^61+2x^62+1x^78

The gray image is a code over GF(2) with n=408, k=13 and d=180.
This code was found by Heurico 1.16 in 0.935 seconds.