The generator matrix

 1  0  1  1  1  4  1 10  1  6  1  1  1 10  1 10  1  2 10  1  1 12  1  1  1 12  1  4  1  6  1  1  0  1  1  1
 0  1  1  0 11  1  6  1 13  1  7  2  1  1  4  1 15 10  1  8  9  1 14  8  6  1  9  0  6  1 10  7  8 14  7  0
 0  0  2  6  0  2  0  2  4  4  6  2  6  2  8  4 12  6  6  8 14  8 14  2 12 14  0  2  2  0 10  0  4  0  2  0
 0  0  0 12  0  4  4  8 12  4 12 12  0  4  4  8  4  4  8  8  4  4  8  8 12  0  8  8  0  4 12  8  4  0  4  0
 0  0  0  0 12  4  4 12  4  8  0 12 12  8  0 12  8  4  0 12 12  4 12  0  0  0  8 12 12 12  4  8 12  4 12  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0  8  8  0  0  0  8  0  0  8  8  8  8  0  0  8  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+61x^28+192x^29+469x^30+1062x^31+2212x^32+4586x^33+7581x^34+10482x^35+12109x^36+10706x^37+7693x^38+4494x^39+2061x^40+1054x^41+494x^42+150x^43+66x^44+38x^45+18x^46+4x^47+2x^48+1x^58

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 21.8 seconds.