The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+171x^28+64x^29+416x^30+492x^31+1149x^32+1724x^33+4372x^34+3868x^35+8243x^36+3852x^37+4444x^38+1732x^39+1152x^40+500x^41+332x^42+52x^43+145x^44+4x^45+36x^46+18x^48+1x^52

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 9.6 seconds.