The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  8  1  1  2  1  2  1  1  2  1  2  1  2  4  2  1
 0  2  0  6  4  6 12  2  8  0  6 14  4  6  2 10  6  2  0 14 10 12 14  0 14 14 10  2 14 10  8  4  0
 0  0 12  0  4  0  0  0  8  4  4  4  8  4 12  4  8  8 12  4  0  0 12  4  8  0 12  0  4  8  4  4  0
 0  0  0 12  0  0  8 12 12 12  4  8 12  4 12  4  0 12 12  8  8 12  8  4 12 12 12 12  8  0  0  0  0
 0  0  0  0  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+74x^27+150x^28+336x^29+567x^30+1032x^31+838x^32+2244x^33+837x^34+1064x^35+512x^36+280x^37+129x^38+64x^39+28x^40+20x^41+3x^42+6x^43+6x^44+1x^48

The gray image is a code over GF(2) with n=264, k=13 and d=108.
This code was found by Heurico 1.16 in 1.85 seconds.