The generator matrix

 1  0  1  1  1  6  1 10  1  1 12  1  1  8  1  2  1  1  1  1  1  1  1 14  1  1  0  2  4  1  1  1  1  1  1  1  1  0  1  8
 0  1 11  6 13  1  2  1 11 12  1 13  8  1  5  1 15  6  9 10  8  2 13  1 15 14  1  1  1  5 14  6  8  6  1 12  8  2  8  1
 0  0 12  0  4  4  8  4  0  8  0  0  4  0 12  4  8  4 12  4  8  8  0 12 12  4 12  8 12  0  4  0  8  8  0 12  0 12  0  8
 0  0  0 12  0  4  4 12  4  0  0  4  8  4 12  8  8 12  4 12  4 12  8  8 12  8 12  4  8  8  4  0  4  8 12  4  0 12 12 12
 0  0  0  0  8  0  8  8  0  8  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+102x^35+375x^36+498x^37+1172x^38+976x^39+2073x^40+902x^41+1122x^42+502x^43+339x^44+62x^45+24x^46+14x^47+8x^48+10x^49+2x^50+4x^51+2x^52+2x^55+2x^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 40.9 seconds.