The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+142x^27+706x^28+1988x^29+4092x^30+7876x^31+10857x^32+13796x^33+11530x^34+7978x^35+3900x^36+1782x^37+592x^38+192x^39+50x^40+32x^41+10x^42+4x^43+6x^44+2x^45

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 26 seconds.