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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+104x^30+256x^31+243x^32+256x^33+392x^34+5675x^36+456x^38+256x^39+204x^40+256x^41+56x^42+20x^44+16x^46+1x^68

The gray image is a code over GF(2) with n=288, k=13 and d=120.
This code was found by Heurico 1.16 in 50.3 seconds.