The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  0  1  2 12  1  1  1  2  1  0  1  1  1  1  2  1  1 12  4  1  1  2  1  1
 0  2 12  6  0  6 12 10  0  6 12  6  2 10 10  2  0  6 10  6 12  2  0 12 12  0 10  6 14  2  0  6  4  6  8  0
 0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  8  0  8  8  0  0  0  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  8  8  0  8  0  0  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  8  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  8  0  0  8  8  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  0  8  8  0  8  8  0  0  8  0  8  8  0  0  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+32x^28+16x^29+147x^30+80x^31+291x^32+368x^33+1277x^34+816x^35+2150x^36+816x^37+1276x^38+368x^39+302x^40+80x^41+104x^42+16x^43+30x^44+9x^46+6x^48+3x^50+4x^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 0.62 seconds.