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

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

Homogenous weight enumerator: w(x)=1x^0+72x^27+149x^28+204x^29+255x^30+356x^31+647x^32+1552x^33+3047x^34+3814x^35+3058x^36+1580x^37+657x^38+362x^39+234x^40+168x^41+96x^42+66x^43+37x^44+16x^45+8x^46+2x^47+2x^48+1x^58

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 3.82 seconds.