The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^29+462x^30+942x^31+2335x^32+4676x^33+6639x^34+11780x^35+11695x^36+11646x^37+7025x^38+4662x^39+2095x^40+896x^41+396x^42+120x^43+61x^44+14x^45+5x^46+5x^48+1x^58

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 22.1 seconds.