The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  8  1  1  1  2  0  1  1  1  1  1  2  1  1  1  2  4  1  0  1  1
 0  2  0  6  0 14  0  6  2 12  6  4 14  2  6  2  8  6  2 14  2  2 12  0 12 10  6  0  4 14 12 12  0  0  0  8
 0  0 12  0  0  0  4  4  4  8  0  4  0  0  4  8 12  4  4  4  4  8  8 12  4  4 12 12  0  8 12  4  4  4  0  8
 0  0  0 12  0  0  0  0  0  0  0  0  8  8  8  8 12 12  4 12 12 12 12  4  8  0 12 12  4  4  4  8  0  0  8  0
 0  0  0  0 12  4  4  4  8  0  0  0 12  8  4  4  4  0  4 12  8 12  4  0  4 12  8  4  8  8  4  0  4  0  4  0
 0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  0  0  8  8  0  8  0  8  8  0  8  0  0  8  8  8  8
 0  0  0  0  0  0  8  8  0  8  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+172x^28+68x^29+540x^30+356x^31+1314x^32+1716x^33+4086x^34+5020x^35+6273x^36+5044x^37+3966x^38+1724x^39+1420x^40+332x^41+466x^42+68x^43+152x^44+8x^45+30x^46+9x^48+3x^52

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 9.93 seconds.