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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+35x^68+2x^69+19x^70+4x^71+2x^73+1x^74

The gray image is a code over GF(2) with n=544, k=6 and d=272.
This code was found by Heurico 1.16 in 0.142 seconds.