The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^34+30x^35+52x^36+50x^37+109x^38+438x^39+672x^40+434x^41+90x^42+42x^43+30x^44+22x^45+18x^46+2x^47+7x^48+6x^49+8x^50+6x^52+1x^70

The gray image is a code over GF(2) with n=320, k=11 and d=136.
This code was found by Heurico 1.16 in 0.142 seconds.