The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  4  4  4  2  2  2  1
 0 12  0  0  0  0  0  0  0 12  4 12 12  8  8  0 12 12  4  8 12  4 12  4  8 12  0  8  0  4  8  4  4  8  0  0
 0  0 12  0  0  0  4 12  4  4  4  8  0  8 12  8  0  0  8  4  0  8 12 12  0  4  0  4 12 12  0  4  4 12  8  4
 0  0  0 12  0  4  4  4  8  4  0 12  4  8  8  0  4  8  8 12  4  8 12 12 12  8  4  4  8  0  4  0  0  4 12  0
 0  0  0  0 12  4  0  4  4  8  0  8 12  0  8 12  8  8  4 12 12 12  0 12  0  8 12  4  0  0  0  8  4  8  4 12
 0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+143x^28+418x^30+44x^31+716x^32+512x^33+1884x^34+2508x^35+3953x^36+2528x^37+1860x^38+516x^39+733x^40+32x^41+348x^42+4x^43+143x^44+34x^46+5x^48+1x^52+1x^56

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 3.26 seconds.