The generator matrix

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

generates a code of length 32 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+144x^27+308x^28+466x^29+924x^30+1338x^31+1947x^32+1318x^33+856x^34+390x^35+255x^36+166x^37+60x^38+14x^39+2x^41+2x^43+1x^52

The gray image is a code over GF(2) with n=256, k=13 and d=108.
This code was found by Heurico 1.16 in 0.529 seconds.