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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+63x^38+107x^40+56x^42+256x^43+1088x^44+256x^45+107x^46+70x^48+8x^50+21x^54+12x^56+1x^62+1x^64+1x^72

The gray image is a code over GF(2) with n=352, k=11 and d=152.
This code was found by Heurico 1.16 in 74.5 seconds.