The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  8  1  1 10  1  1  2 12  1  4  2  1  8 12  1  4  1 10  4  6  8
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  1  3  6  1  1  4  1  1  5  1  1  2  1  1 12  1  9  1  2  1  1
 0  0 12  0  0  0  0  4  4 12 12  0  8  8  8  0  8  4  4  4  4  0  0  4  0  0  4 12 12 12 12  8  8  4  0  8
 0  0  0 12  0  4  4  4 12 12  8  0  4  8  4  4  0  4 12  8  8  4  0 12 12 12  0  0  4 12  8  0  0  8  8  4
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  0  0  8  8  0  8  8  0  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  8  0  0  8  0  0  8  0  0  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+177x^28+28x^29+528x^30+596x^31+1827x^32+3740x^33+6836x^34+13044x^35+11950x^36+13044x^37+6916x^38+3740x^39+1856x^40+596x^41+412x^42+28x^43+174x^44+28x^46+12x^48+2x^52+1x^60

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 23.7 seconds.