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

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

Homogenous weight enumerator: w(x)=1x^0+101x^28+215x^32+64x^34+448x^36+6528x^38+492x^40+64x^42+147x^44+124x^48+7x^52+1x^68

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 0.968 seconds.