The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+38x^29+199x^30+232x^31+652x^32+1006x^33+1872x^34+2860x^35+2793x^36+2806x^37+1850x^38+960x^39+614x^40+226x^41+160x^42+44x^43+30x^44+20x^45+15x^46+5x^48+1x^52

The gray image is a code over GF(2) with n=288, k=14 and d=116.
This code was found by Heurico 1.16 in 2.33 seconds.