The generator matrix

 1  0  1  1  1  4  2  1  1  1  1 10  1  1  0  1  4  1  1  1  1  1  1  6  4  1  1  2  1  2 10  1  2  1  1  1
 0  1  1  6 15  1  1  4  3  2  5  1  4 15  1  6  1  7  4  6 12  7  7  1  1  9  5  1  2  2  1 10  4 10  5  0
 0  0  2  0  2  6  2 10  8  6  4 12  4 14  4  0 10  2 14  6 12  8 12  2  8 10  4  0 12 10  6  8 14 12 14  8
 0  0  0 12  4  4  8  0  0  4 12  4  8 12  8  8  8  8  4  0  4  4  0 12  4 12  0  8  4  0  0  0 12 12 12  0

generates a code of length 36 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+48x^31+254x^32+628x^33+1118x^34+1566x^35+1307x^36+1282x^37+1009x^38+576x^39+228x^40+100x^41+32x^42+18x^43+15x^44+6x^45+1x^46+3x^48

The gray image is a code over GF(2) with n=288, k=13 and d=124.
This code was found by Heurico 1.16 in 0.467 seconds.