The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  1  1  1  1  2  1  2  1  1  4  2
 0 12  0  0  0  4 12 12  8  8  0  0  4  4  4 12  8  4 12  4  8 12  8 12  0  4 12  0  0 12  4  4
 0  0 12  0  4  4  4  0  8  0  4 12  4  4  0  8  0 12  4  8  8  4  8  0  8  0 12 12  4  8  0  0
 0  0  0 12  4  8  4  4  0  4  4  0  0 12  4  8  4  0  8  0  4 12  0  8  0  4 12  8  8  4 12 12
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+164x^28+64x^29+36x^30+448x^31+661x^32+448x^33+24x^34+64x^35+99x^36+4x^38+34x^40+1x^52

The gray image is a code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 1.7 seconds.