The generator matrix

 1  0  1  1  1 14  1  1  4  1  1 10  6  1  1  1  1  2  0  1  1  0  1 14  1  1 12  2  1  1  2  1  4  1  1  6  1  1  0  1
 0  1  1  0  7  1  2  3  1  6  5  1  1  4  3  2  9  1  1  1 11  1 10  1  0  9  1  0 14 15 10  3  1 11 12  1  8  4  4  0
 0  0  2  6  2  4 14  0  2  0  8  6  8  2 12  8 10  6 12  0  6  6 14 12  4  6  6 14 12  0 14  6 10  2  0  6 14 12  2  0
 0  0  0 12  0  0 12  0  8  8  8  0  0  8 12  4 12  4 12 12  4  8  8 12 12  0 12 12  0  4  0  8  0 12  4  4  4  4  4  0
 0  0  0  0  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  0  8  8  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+80x^34+294x^35+772x^36+1312x^37+1795x^38+2372x^39+2870x^40+2802x^41+1985x^42+1102x^43+522x^44+260x^45+127x^46+40x^47+23x^48+10x^49+11x^50+2x^52+2x^54+2x^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 1.87 seconds.