The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  1  1  0  1  6  1  1  0  1  2  0  0
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 12 15  1 10  9  0  3  1 12  1  6 15  1  5  0  1  1
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  8  8  8  0  0  8  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  8  0  0  0  0  8  8  8  0  0  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  0  0  8  0  8  0  0  8  8  8  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  0  0  0  8  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+108x^28+8x^29+220x^30+120x^31+1063x^32+1768x^33+4508x^34+4760x^35+7673x^36+4760x^37+4532x^38+1768x^39+1021x^40+120x^41+212x^42+8x^43+90x^44+26x^48+1x^52+1x^56

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 5.76 seconds.