The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  2  1  4  1  1  1  0  2  4  1  1  1  2  4  2  1  2  1  1  2  2  1  1
 0 12  0 12  0 12  0 12  0 12  0  4  8 12 12 12 12  0 12 12 12 12  4  0  4 12 12  0 12  4  0 12 12  8  0 12  0  8 12  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  8  0  0  0  0  8  0  8  0  8  0  0  0  8  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  0  0  0  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  0  0  8  8  8  0  8  0  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  0  0  0  8  8  0  8  8  8  8  0  0  0  8  0  0  0  8  0  8  8  8  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  0  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  8  8  8  8  0  8  8

generates a code of length 41 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+100x^28+48x^30+363x^32+280x^34+64x^35+1038x^36+640x^37+1820x^38+1984x^39+8723x^40+2816x^41+8304x^42+1984x^43+2327x^44+640x^45+648x^46+64x^47+539x^48+152x^50+177x^52+12x^54+37x^56+5x^60+1x^64+1x^68

The gray image is a code over GF(2) with n=328, k=15 and d=112.
This code was found by Heurico 1.16 in 12.9 seconds.