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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+53x^38+97x^40+81x^42+56x^43+95x^44+56x^45+96x^46+280x^47+98x^48+6424x^49+113x^50+168x^51+88x^52+168x^53+85x^54+8x^55+77x^56+8x^57+57x^58+39x^60+22x^62+15x^64+4x^66+2x^68+1x^82

The gray image is a code over GF(2) with n=392, k=13 and d=152.
This code was found by Heurico 1.16 in 1.5 seconds.