The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^28+16x^29+236x^30+112x^31+1023x^32+336x^33+3220x^34+560x^35+5142x^36+560x^37+3228x^38+336x^39+984x^40+112x^41+220x^42+16x^43+116x^44+8x^46+24x^48+2x^52

The gray image is a code over GF(2) with n=288, k=14 and d=112.
This code was found by Heurico 1.16 in 26.7 seconds.