The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+63x^28+162x^29+343x^30+652x^31+1373x^32+1792x^33+4250x^34+3488x^35+8418x^36+3564x^37+4291x^38+1888x^39+1348x^40+608x^41+308x^42+112x^43+55x^44+18x^45+21x^46+4x^47+6x^48+2x^50+1x^54

The gray image is a code over GF(2) with n=288, k=15 and d=112.
This code was found by Heurico 1.16 in 8.35 seconds.