The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  1  1  0  1  6  1  1  1 12  1 10  1  1  1  0  1 10  1  1 12  1  1  6  1  1  1  1  1  1  6  1  1  1  1  2  1  0  1  1 10  1  1  1  0  1  8  8  1  2  1  2  1  0  1  1
 0  1  3  6  5  1 12 15  1  9  1 10  6  0  3  1  5  1 12 10 15  1  9  1  6  0  3  1  5  1 12 10  1 15  9  1  6  0  8 10 12  3  1  6 12  6 14  0  5  1 15  4  1 14  0 10  1 15  2  2  6  6 14 10  2  2 10  0
 0  0  8  0  0  0  0  0  8  8  8  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  8  0  0  8  0  0  0  0  8  0  8  8  8  0  8  0  0
 0  0  0  8  0  0  8  0  0  8  8  0  8  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  8  0  0  0  0  8  0  8  8  0  0  8  0  0  8  8  8  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  0  8  0
 0  0  0  0  8  0  8  8  8  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  8  0  8  8  0  0  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  8  8  0  0  0  0  0  8  8  8  8  0  8  0  0  0  0  8  8  8  0  8  8  8  0  8  8  8  8  0  0  8  0  8  0  0  8  0  0  0  0  8  0  0  0  8  8  0  8  8  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+38x^62+128x^63+355x^64+236x^65+555x^66+396x^67+744x^68+424x^69+475x^70+232x^71+300x^72+108x^73+75x^74+12x^75+6x^76+6x^78+1x^82+1x^86+2x^92+1x^106

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 0.372 seconds.