The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  2  1  8  1  2  1  1 14  1  1  1  1  8  1  0  4  1  1  8  1  2  8  1  1  1
 0  1  1  4  3  1  2  7  1  5 14  1  8  1 11  1 10  6  1 13 15  6 15  1 11  2  4  7  8  1 11  0  2  9 15  0
 0  0  2  2  0  2  2 10  0  8  4  2  4  4 10  4  6 14 10 12  8  0  6  2 12  6  2  4  4  0 12 10 14 10 14  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0
 0  0  0  0  8  0  8  8  8  0  8  8  8  0  8  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  8
 0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  0  8  8  0  8  8  0  0  0  0  8  0  0  8  8  0  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+36x^30+278x^31+566x^32+1266x^33+1755x^34+2780x^35+3068x^36+2944x^37+1675x^38+1134x^39+438x^40+258x^41+113x^42+32x^43+20x^44+12x^45+5x^46+3x^48

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 1.5 seconds.