The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+241x^32+184x^34+256x^35+728x^36+256x^37+192x^38+141x^40+8x^42+32x^44+8x^48+1x^56

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 34.4 seconds.