The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+72x^28+332x^29+665x^30+1364x^31+2291x^32+3816x^33+7886x^34+9360x^35+13946x^36+9208x^37+8027x^38+4112x^39+2252x^40+1160x^41+591x^42+256x^43+90x^44+76x^45+12x^46+12x^47+4x^48+3x^50

The gray image is a code over GF(2) with n=288, k=16 and d=112.
This code was found by Heurico 1.16 in 31.1 seconds.