The generator matrix

 1  0  1  1  1  4  1  1  6  1  1 10  1  1  1  1 10  1  0 12  1  2  1  1 12 14  1  1  4  1  0  2  1  1  1  1
 0  1  1  0 11  1 10  5  1  7  6  1  2  7  8 13  1 14  1  1 13  4  0  8  1  1 15  0  2  5  1  4 13  7  1  0
 0  0  2  6  4  6 14  4  0  6  4  6  6 10  4  0 12  8  4 14 14  6  2 10  0  2  0  2  6 12 12 10  0  2  0  0
 0  0  0 12  0  4  0 12  0  4  4  8  4  8  8  4  4  4 12  8  4 12 12  8  0  8  8 12  0  4 12  8 12  8  4  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  8  8  8  0  0  8  0  0  8  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+87x^28+174x^29+315x^30+1078x^31+2041x^32+4456x^33+7802x^34+9986x^35+13280x^36+10546x^37+7909x^38+4318x^39+1918x^40+974x^41+338x^42+166x^43+81x^44+40x^45+15x^46+4x^47+2x^49+4x^50+1x^54

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 21.3 seconds.