The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  2  2  1  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  0  0  8
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  0  8  0  0  0  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  0  8  0  8  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  0  8  0  8  8  8  8  0  8  8  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8  0  0  0  0  0  8  0  8  0  0  0  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  0  8  8  8  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  0  0  8  0  0  8  0  8  8  8  8  0  8  0  8  8  0  8  8  0  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  8  8  8  0  8  8  0  0  0  0  8  8  0  0  8
 0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  8  8  0  8  8  8  8  8  8  0  8  0  0  0  8  8  8  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+46x^26+106x^28+144x^30+184x^32+211x^34+256x^35+223x^36+768x^37+12500x^38+768x^39+222x^40+256x^41+236x^42+184x^44+134x^46+89x^48+35x^50+15x^52+5x^54+1x^70

The gray image is a code over GF(2) with n=304, k=14 and d=104.
This code was found by Heurico 1.16 in 3.56 seconds.