The generator matrix

 1  0  1  1  1 12  1  1  2  1 14  1 12  1  1  1  1 10  1  1  1  1  8  1  1  1  1  4 12  1 14  4  1  4  2  1
 0  1  1 12 11  1  2  7  1 14  1 13  1  4  4  9  9  1  3  7  2  5  1 10  3  6  7  1  2 11  1  2  9  2  4  0
 0  0  2  6  4  6  2 14  2  4  4  4  0  2 12  6  0  6  0  2  4  0  2  6  6  0  4 10  6  2 10  2  8  2  2  0
 0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  8  0  8  0  8  8  8  0  0
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  0  8  8  8  8  8  0  0  0  0  0  8  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  8  0  0  0  8  8  0  0  8  0  8  0  8  8  8  8  0  8  0  0  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+64x^28+188x^29+477x^30+1022x^31+1834x^32+4926x^33+6994x^34+12314x^35+9968x^36+12262x^37+6955x^38+4950x^39+1882x^40+1034x^41+392x^42+142x^43+72x^44+22x^45+23x^46+4x^47+3x^48+6x^50+1x^54

The gray image is a code over GF(2) with n=288, k=16 and d=112.
This code was found by Heurico 1.16 in 20.8 seconds.