The generator matrix

 1  0  0  1  1  1  2 12  1  1 10  1  1  4  1  1  1  1 12  2  0  0  1  1  1  1  1  1  8  8  6 10  1  1  6  1
 0  1  0  2  1  7  1  1  4 10  1 11 13  2  3  0  5 10  1 14  8  1  4  8  0  9 15  5  1  1  1  8  7  4  1  0
 0  0  1  1  3  2  1  2  6  3  7  7  6  1  4  5  9  2  5  1  1  6  2  1  4  1 13  6  3  8  1  1  0  9  4  0
 0  0  0  4  0  4  4  0  0  4  4  8 12  4  0  8 12  4  8  0  4  4  4  8 12 12 12  8  0  8  8 12  8  0 12  0
 0  0  0  0  4  4 12 12 12 12  8  8  8  4  4  8 12  8  0  4  8  4 12 12  8  0  0  8 12  4 12  4  4  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+32x^29+329x^30+914x^31+2355x^32+4468x^33+7559x^34+10274x^35+13100x^36+10900x^37+8029x^38+4254x^39+2092x^40+780x^41+261x^42+102x^43+52x^44+12x^45+14x^46+8x^47

The gray image is a code over GF(2) with n=288, k=16 and d=116.
This code was found by Heurico 1.16 in 17.9 seconds.