The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2 12  2  8  2  4  1  1  1  1  2  2  2  2  1  1  1  1  4  4  0  8  1  1  1  1
 0  2 12  6  8 14  4 10  0  6 12 10  8 14  4  2  6  2 10  2 14  2  2  2  0 12  8  4  0 12  8  4  6 10 14  2 12  4  4  4  0  8  6 14

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

Homogenous weight enumerator: w(x)=1x^0+118x^44+4x^46+4x^50+1x^56

The gray image is a code over GF(2) with n=352, k=7 and d=176.
This code was found by Heurico 1.16 in 0.0398 seconds.