The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^30+104x^32+56x^34+256x^35+1088x^36+256x^37+112x^38+75x^40+8x^42+20x^46+11x^48+1x^56

The gray image is a code over GF(2) with n=288, k=11 and d=120.
This code was found by Heurico 1.16 in 15.1 seconds.