The generator matrix

 1  0  0  1  1  1  4  8  1  1  1  1 12 14 14  1  6  1  2  1  1  4  1  1 14  1  4  1  0  4  1  1  1
 0  1  0  1 14 11  1  1  2  5  6  9  1 10  1 15  1  1 12  4  8  4  7  3  1 15  1  4  1 10  3 12  0
 0  0  1  1  5  4  7  4  4 10  1  7 15  1  4  6  1  6  1  1  8  1 11 15 11 10  8  9 12  1  3 10  0
 0  0  0  2 10  0  8  6 14  6  4  4  2 14 12  6  4 12  8  4  2  6  4 10  2  0  6 10 12 12  0 10  0
 0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  8  0  0  8  8  0  0  0  8  0  0  8  8  0  0  8  0  8

generates a code of length 33 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+130x^27+859x^28+1874x^29+3874x^30+7718x^31+11443x^32+13644x^33+11697x^34+7708x^35+3845x^36+1738x^37+708x^38+182x^39+74x^40+24x^41+9x^42+6x^43+2x^44

The gray image is a code over GF(2) with n=264, k=16 and d=108.
This code was found by Heurico 1.16 in 16.1 seconds.