The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+234x^35+363x^36+722x^37+972x^38+1272x^39+1271x^40+1272x^41+881x^42+568x^43+243x^44+194x^45+94x^46+80x^47+9x^48+4x^49+5x^50+6x^51+1x^56

The gray image is a code over GF(2) with n=320, k=13 and d=140.
This code was found by Heurico 1.16 in 1.47 seconds.