The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^29+474x^30+926x^31+2112x^32+4222x^33+7620x^34+10802x^35+12822x^36+11102x^37+7770x^38+4118x^39+2022x^40+826x^41+384x^42+150x^43+62x^44+10x^45+8x^46+4x^47+5x^48

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 22.3 seconds.