The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+181x^28+372x^30+1127x^32+256x^33+2618x^34+1792x^35+3761x^36+1792x^37+2514x^38+256x^39+1174x^40+350x^42+145x^44+34x^46+10x^48+1x^52

The gray image is a code over GF(2) with n=288, k=14 and d=112.
This code was found by Heurico 1.16 in 3.31 seconds.