The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  2 12  2  1  1  2  8  1  2  8  1  1  1 12  1  1  1
 0  2  0  0  0  2  6 14  8  8 14  2  6  4  8  6  4  2 14  0  2 10 10 10 12  2 10  2  2 12  6 10  2  2  2  8
 0  0  2  0  2  2 10  0 12 14  8 14  2 12  6  4  8 10  6 12  4 12 14  0 10 12 14  6  4  6 14  2  0  0 12  0
 0  0  0  2  2  8 10  2  4  0 14  2  8  2  2  0 10 12  2 10  4 10  4 10  8 14 14 10  4 10  0 10  2 12  6  0
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0  8  8  8  0  8  0  8  0  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+139x^30+374x^31+728x^32+1022x^33+1770x^34+2688x^35+2948x^36+2766x^37+1806x^38+1008x^39+587x^40+266x^41+186x^42+56x^43+19x^44+10x^45+3x^46+2x^47+4x^48+1x^52

The gray image is a code over GF(2) with n=288, k=14 and d=120.
This code was found by Heurico 1.16 in 2.28 seconds.