The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  8  1  1 14  1  1  4  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  8 11  1 14 13  1  4  7  1  2  1  1  0  6  3  5 12 10 15  9  8 14  4  2 11 13  7  1  0  6 12 10

generates a code of length 44 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+32x^43+188x^44+32x^45+1x^48+1x^56+1x^72

The gray image is a code over GF(2) with n=352, k=8 and d=172.
This code was found by Heurico 1.16 in 0.0174 seconds.