The generator matrix

 1  0  1  1  1 12  1  1  2  1  6  1  1  1  1  1  4  1  8  1  4  1  1  1  1  1  1  0 12  1  1  1  1  0  4  1
 0  1  1 12 11  1  2  5  1  6  1  7 13  3 15  0  1  4  1 14  1 11  1 14  1  6  5  2  2  4 11 13  8  2  1  0
 0  0  2  6  4  6  2  0 10  0  8  2  4  6  0  6  2  4 10  4  4 10 12 10  2  8  0  6  6  2  6 10 10 14 12  0
 0  0  0  8  0  0  0  8  8  0  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  0  8  8
 0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  8  8  0  8  8  0  8  0  0  0  8  0  8
 0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8
 0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+34x^29+168x^30+594x^31+1119x^32+1758x^33+4128x^34+4854x^35+7626x^36+4652x^37+4122x^38+1886x^39+1094x^40+456x^41+146x^42+90x^43+14x^44+10x^45+6x^46+2x^48+2x^49+6x^50

The gray image is a code over GF(2) with n=288, k=15 and d=116.
This code was found by Heurico 1.16 in 5.78 seconds.