The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1  4 10  1  1 12  6  1  1  1  1  1  1  1  1  1  2  8  8  1  2  2  1
 0  1 11 14  5  1  0  3  1  6  1  9 13  4  1  1  7 10  1  1  5  2 15  9  8 11  6  3  4  1  1  1  6 14  8  0
 0  0 12  4  0  4 12  0  8  8 12  0  4  4  4  0  4  8  8  0  0  4  0  0  4 12  8  0  4  4 12  4  0  4  4  0
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  0  0  8  8  0  8  8  8  8  0  0  8  0  0  0  0  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  8  0  0  8  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  8  0  8  0  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  0  8  8  0  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  8  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+60x^28+92x^29+139x^30+426x^31+761x^32+2576x^33+3634x^34+5712x^35+6140x^36+5528x^37+3738x^38+2468x^39+676x^40+496x^41+144x^42+96x^43+40x^44+12x^45+19x^46+2x^47+2x^48+6x^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 5.88 seconds.