The generator matrix

 1  0  1  1  6  1  1  1 10  1  1 12  1  1  8  1  1  1 12 14  1  1  1  8 10 12  2  1  0  1 10  2  2  4  1  1
 0  1  1  6  1  3  5  4  1  2 15  1 14 13  1 11 13  6  1  1  4 11 14  4  1  1  8  0  1 12  1  4  6  1  6  0
 0  0  2  0  0  8  8  2  6 10  6  6 12  4  4 10 10 14 10 10 12 12  2  2  0 12  2  0  4  8  6 14  6  2  2  0
 0  0  0  8  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  0  8  8  8  0  8  0  8  0  0  0
 0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+52x^31+370x^32+580x^33+1162x^34+1218x^35+1606x^36+1134x^37+1100x^38+496x^39+310x^40+72x^41+42x^42+26x^43+14x^44+6x^45+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 0.438 seconds.