The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^27+138x^28+388x^29+569x^30+1262x^31+2219x^32+3682x^33+4288x^34+7636x^35+4220x^36+3800x^37+2182x^38+1248x^39+564x^40+316x^41+116x^42+56x^43+26x^44+4x^45+9x^46+2x^47+2x^49+4x^50

The gray image is a code over GF(2) with n=280, k=15 and d=108.
This code was found by Heurico 1.16 in 9.69 seconds.