The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  8  8  2  1  2  1  0  1  1  2  1  1  1  4  1  1  1
 0  2  0  2  0  0  6 14  0 12  6  2  6  8 12  2  4  6  2  4  2  8  4  6  6  4  2  4 14  6  6  6 12  0  8  0
 0  0  2  2  0 14  6  0  4  2  0  6 10  4 14  8  2  0  6  2  4 10  0  2 12  2 10  2  8  6  4  6  2  0  2  0
 0  0  0  4 12  4  0  4 12  4  8  4  8  8  0 12  0  0 12  8  8 12  0 12  4 12  4  0 12 12 12  0  8 12  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  0  0  0  8  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  0  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+61x^28+164x^29+402x^30+592x^31+1036x^32+1886x^33+3499x^34+5544x^35+6402x^36+5496x^37+3579x^38+2036x^39+922x^40+504x^41+356x^42+144x^43+89x^44+12x^45+34x^46+4x^47+1x^48+2x^49+1x^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 8.48 seconds.