The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+41x^26+52x^27+140x^28+222x^29+250x^30+328x^31+571x^32+846x^33+5146x^34+1158x^35+5150x^36+922x^37+567x^38+334x^39+250x^40+170x^41+115x^42+46x^43+30x^44+16x^45+22x^46+2x^47+2x^48+2x^50+1x^54

The gray image is a code over GF(2) with n=280, k=14 and d=104.
This code was found by Heurico 1.16 in 2.94 seconds.