The generator matrix

 1  0  0  1  1  1  2  1  1 14  1  1  4  4  1  1  6 12  2  1  1  1 12  1  1  2  1  8  1  2  1  8  1  1  4  1
 0  1  0  2 13  7  1  6  9  1  6 11  1  2 12  8  4  1  1  3 11 12  1  3  0  1  9  1 15  1  7  1  8 13  1  0
 0  0  1  1 11  2  1  0  6  4  7  3  1  1  1  6  1  2  8  8  1  3  5 12 12  3 11  0 14  9 15  1  4  8  5  0
 0  0  0  4 12  0  8  0  0  0  4  4  8  0 12  4 12  4  4  8  8  0  8  4  8 12  0  0  4 12  0 12  0  4 12  8
 0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8
 0  0  0  0  0  8  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+56x^29+286x^30+772x^31+2134x^32+3868x^33+8443x^34+10180x^35+14062x^36+10136x^37+8682x^38+3882x^39+1864x^40+710x^41+308x^42+72x^43+50x^44+12x^45+8x^46+6x^47+1x^48+2x^49+1x^50

The gray image is a code over GF(2) with n=288, k=16 and d=116.
This code was found by Heurico 1.16 in 17.7 seconds.