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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+14x^29+38x^30+46x^32+70x^33+768x^34+42x^37+21x^38+14x^40+2x^41+4x^46+3x^48+1x^54

The gray image is a code over GF(2) with n=272, k=10 and d=116.
This code was found by Heurico 1.16 in 7.05 seconds.