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  8  1  0  1  1  1  1  1  2  1  1  1  1  1  2  1  1  4  1  2  1  1 12  1  8  1 12  1  1  1  2  8  4  1  0  8  2  2
 0  2  0  6  4  6 12  2  0  6  8 14  4  2  4 10  8  2  6 12  0  2 12 14 14 12 10  4 14  0  2  0  2  6  2 12  8  6 14  4 10  6  6  8  4  4  2  2  8  6  4  4  2  8  2  4  2  4 12 12  0  2  2 12  2  2  6 14
 0  0 12  0  4  0  8  0  4  4  0  4  4 12  0 12  8  4  8  0  4  0  4  4  8 12  4  0 12 12 12  8  8  8 12  8  0  4  0  4  4  8  4  0  4  4  8 12  8  0  0  0 12  4  8  4  8 12  0  8  4 12  0 12  8  0  8  0
 0  0  0 12  0  8  8  4  4  4  4  0 12  0  4  4 12  0  8  0 12  4  8  4 12  4  4 12  0  8  8  0  0  8  4  0  4  8  4 12  8  0  0  0  4  8 12  8  4  0  8  4 12  0 12  4  8  4 12  4  8  8 12  8  4 12  0  4
 0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  0  8  8  8  0  0  8  8  0  0  8  8  8  0  0  8  0  0  0  8  8  0  0  8  8  0  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  0  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+84x^62+128x^63+369x^64+164x^65+746x^66+252x^67+808x^68+168x^69+634x^70+216x^71+304x^72+52x^73+62x^74+44x^75+28x^76+10x^78+20x^80+4x^84+1x^88+1x^104

The gray image is a code over GF(2) with n=544, k=12 and d=248.
This code was found by Heurico 1.16 in 0.737 seconds.