The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+68x^27+290x^28+740x^29+1253x^30+2388x^31+3775x^32+6956x^33+11398x^34+11312x^35+11829x^36+7192x^37+3916x^38+2372x^39+1004x^40+588x^41+258x^42+116x^43+56x^44+12x^45+7x^46+4x^48+1x^52

The gray image is a code over GF(2) with n=280, k=16 and d=108.
This code was found by Heurico 1.16 in 29 seconds.