The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  1  0  1  1  1  2  1  4  1  2 12  1  1  1  1  8  8  1  2  2  1
 0  2  0 14  4  6 12  2  0  6 14 12  6  2 14  8  2  2 14 10 10  4  2  0  6  2 12  6  8 14  2  2 14  8 12  4
 0  0 12  4  4  0  0  4  0  0  4  8  0  4  4  4  8  4  4  0  0  4 12  8  8  8  8  8 12  4  4  4  4  4 12  4
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  8  8  8  8  0  8
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  8  0  0  8  0  8  8  0  8  0  8  8  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  0  8  8
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  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+222x^28+68x^29+358x^30+448x^31+1117x^32+1584x^33+4688x^34+4032x^35+7736x^36+4056x^37+4620x^38+1600x^39+1240x^40+432x^41+288x^42+64x^43+150x^44+4x^45+30x^46+26x^48+4x^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 14.5 seconds.