The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+47x^28+88x^29+219x^30+330x^31+705x^32+1374x^33+1550x^34+2844x^35+2128x^36+2814x^37+1608x^38+1344x^39+634x^40+314x^41+190x^42+84x^43+65x^44+18x^45+13x^46+6x^47+4x^48+4x^50

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 2.57 seconds.