The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^28+52x^29+118x^30+162x^31+317x^32+528x^33+777x^34+1318x^35+1607x^36+1312x^37+772x^38+514x^39+278x^40+144x^41+102x^42+50x^43+48x^44+12x^45+22x^46+4x^47+4x^48+1x^50+1x^52

The gray image is a code over GF(2) with n=288, k=13 and d=112.
This code was found by Heurico 1.16 in 0.767 seconds.