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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+56x^62+94x^64+64x^66+256x^67+1152x^68+256x^69+112x^70+24x^78+32x^80+1x^128

The gray image is a code over GF(2) with n=544, k=11 and d=248.
This code was found by Heurico 1.16 in 30.6 seconds.