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

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

Homogenous weight enumerator: w(x)=1x^0+173x^28+4x^29+394x^30+128x^31+872x^32+668x^33+2076x^34+2312x^35+3261x^36+2172x^37+2060x^38+752x^39+832x^40+100x^41+364x^42+8x^43+157x^44+34x^46+15x^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 3.3 seconds.