The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1  2  1  1  4  1  1  1  0  1  1  2  1  1  2  2  1
 0 12  0 12  0 12  0 12  8  4  0 12  0 12 12  0 12 12  4  4 12  4  4 12  0  8  0  4  4 12  8  8 12 12 12  4
 0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  0  0  0  8  8  8  8  0  8  8  8  0  8  8  0  0  0  8
 0  0  0  8  0  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  8  8  0  0  8  8  0  8  8  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  0  0  8  8  0  8  8  8  0  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  8  8  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+32x^29+60x^30+80x^31+104x^32+152x^33+184x^34+1264x^35+320x^36+1272x^37+240x^38+176x^39+75x^40+72x^41+8x^42+16x^43+8x^45+20x^46+11x^48+1x^56

The gray image is a code over GF(2) with n=288, k=12 and d=116.
This code was found by Heurico 1.16 in 55.9 seconds.