The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+32x^34+64x^35+22x^36+4x^38+1x^40+4x^42

The gray image is a code over GF(2) with n=280, k=7 and d=136.
This code was found by Heurico 1.16 in 0.0137 seconds.