The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+60x^28+44x^30+202x^32+320x^34+256x^35+899x^36+1792x^37+1064x^38+1792x^39+890x^40+256x^41+320x^42+180x^44+44x^46+59x^48+11x^52+2x^60

The gray image is a code over GF(2) with n=304, k=13 and d=112.
This code was found by Heurico 1.16 in 0.849 seconds.