The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1  0  1  1 10  6  1  1  1 10  1  2  2  2  0  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15  1  9 10  1  1  0  6 10  1  5  6  0  0  1  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  0  8  0  0  8  0  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8  8  8  0  8  8  8  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  8
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  8  8  0  8  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+21x^28+32x^29+119x^30+74x^31+575x^32+1050x^33+1919x^34+2946x^35+2937x^36+2930x^37+1940x^38+1054x^39+534x^40+78x^41+100x^42+22x^43+25x^44+6x^45+13x^46+2x^48+5x^50+1x^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 1.48 seconds.