The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^28+68x^29+656x^30+508x^31+1622x^32+1936x^33+3704x^34+4640x^35+5913x^36+4644x^37+4066x^38+2012x^39+1553x^40+456x^41+520x^42+72x^43+161x^44+42x^46+8x^48+4x^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 9.93 seconds.