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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+182x^28+473x^32+924x^36+768x^38+1941x^40+24576x^41+1024x^42+1712x^44+256x^46+582x^48+244x^52+74x^56+10x^60+1x^72

The gray image is a code over GF(2) with n=328, k=15 and d=112.
This code was found by Heurico 1.16 in 15 seconds.