The generator matrix

 1  0  1  1  1  6  1 12  1 10  1  1  1  1  8  1 14  1  1 14  1  1  1  8  4  1  2  1  8  1  1  1  1  2  1 12
 0  1 11  6 13  1  2  1 12  1 11  5  3  8  1 13  1  9  6  1  9  0  4  1  1  7  1  1  1  5 12  8 11  8  5  1
 0  0 12  0  4  4  8  0  8 12  0  0  4 12 12  0  8  0 12 12  4 12  4  0 12  8  8 12  8  4 12  0  4  0  8  0
 0  0  0 12  0  4  4  0  0 12  4  8  4  8  8  4 12  8 12  8 12 12  8 12 12 12  0  0 12  4  4  4  8 12  4  8
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+86x^31+260x^32+614x^33+901x^34+1626x^35+1305x^36+1606x^37+866x^38+578x^39+213x^40+74x^41+22x^42+14x^43+7x^44+10x^45+2x^46+6x^48+1x^50

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 0.502 seconds.