The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  0  1  1  1  1  6  1 14  1 10  1  1  1  1  4  1  8  0  2  0  2  1  2  1
 0  1 11  6  1  1  0  3  1 14  1  5  1 14 11  8 11  1 10  1  6  1  5  2  7  7  1 10  1  2  2  2  0  1  8  0
 0  0 12  0  0  0  0  0  0  8  8  4  4 12  8 12 12  4 12 12  0  8  8  0  4  8  4  8  4  4 12 12  0  8  4  0
 0  0  0 12  0  0 12  8 12  8  4  4 12  0 12 12  4  8 12  4 12 12  0  4  0 12  0 12  8 12  0  4 12  8  4  0
 0  0  0  0  4  4 12  8  4 12  0  8  8  0  8  4  4  4  8  4 12 12  8  8  8  0  8  4  8  4  8  8  4 12  4  0
 0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  8  0  0  0  0  8  8  8  0  0  8  0  0  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^28+98x^29+242x^30+584x^31+977x^32+2036x^33+4182x^34+4934x^35+6372x^36+5046x^37+4449x^38+2044x^39+872x^40+472x^41+199x^42+110x^43+47x^44+28x^45+13x^46+8x^47+2x^48+3x^50

The gray image is a code over GF(2) with n=288, k=15 and d=112.
This code was found by Heurico 1.16 in 6.2 seconds.