The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^43+82x^44+8x^46+4x^48+4x^51+1x^56

The gray image is a code over GF(2) with n=352, k=7 and d=172.
This code was found by Heurico 1.16 in 0.0283 seconds.