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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+53x^32+75x^34+192x^35+400x^36+192x^37+62x^38+24x^40+23x^42+1x^44+1x^68

The gray image is a code over GF(2) with n=288, k=10 and d=128.
This code was found by Heurico 1.16 in 0.0375 seconds.