The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^29+216x^30+910x^31+1968x^32+4406x^33+7468x^34+11544x^35+12446x^36+11466x^37+7522x^38+4588x^39+1884x^40+706x^41+202x^42+104x^43+18x^44+12x^45+14x^46+6x^47+3x^48+2x^50

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 18 seconds.