The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+210x^34+384x^35+760x^36+1104x^37+2150x^38+2192x^39+2905x^40+2332x^41+1910x^42+1064x^43+756x^44+272x^45+202x^46+72x^47+41x^48+4x^49+24x^50+1x^56

The gray image is a code over GF(2) with n=320, k=14 and d=136.
This code was found by Heurico 1.16 in 2.67 seconds.