The generator matrix

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

generates a code of length 32 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+301x^28+72x^29+718x^30+448x^31+1103x^32+432x^33+660x^34+64x^35+211x^36+8x^37+62x^38+15x^40+1x^48

The gray image is a code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 3.09 seconds.