The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  1  1  1  4  2  2  2  4  4  8  1  2
 0 12  0  0  0  0  0  0  0 12  4 12 12  8  8  0 12 12  4  8 12  4  0  4  4  4  8  4 12  0  4  4  4 12  8
 0  0 12  0  0  0  4 12  4  4  4  8  0  8 12  8  0  0  8  4  0  8 12 12 12  8  0 12  0  8 12  0  0  4 12
 0  0  0 12  0  4  4  4  8  4  0 12  4  8  8  0  4  8  8 12  4  8  8 12 12  4  4  4  0  8  4  0  0  0  0
 0  0  0  0 12  4  0  4  4  8  0  8 12  0  8 12  8  8  4 12 12 12  8 12  8 12  8 12  8 12 12 12  4  0  4
 0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+72x^27+146x^28+226x^29+295x^30+440x^31+996x^32+1850x^33+2668x^34+3040x^35+2661x^36+1820x^37+1018x^38+472x^39+250x^40+180x^41+108x^42+72x^43+40x^44+18x^45+7x^46+1x^48+2x^49+1x^52

The gray image is a code over GF(2) with n=280, k=14 and d=108.
This code was found by Heurico 1.16 in 13 seconds.