The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^28+70x^29+135x^30+440x^31+541x^32+1346x^33+1664x^34+2740x^35+2442x^36+2772x^37+1628x^38+1364x^39+518x^40+412x^41+142x^42+60x^43+23x^44+6x^45+13x^46+4x^47+12x^48+2x^49+2x^50+2x^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 2.54 seconds.