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

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

Homogenous weight enumerator: w(x)=1x^0+117x^62+108x^63+223x^64+264x^65+620x^66+268x^67+973x^68+272x^69+573x^70+260x^71+175x^72+104x^73+73x^74+4x^75+27x^76+22x^78+8x^80+3x^82+1x^112

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 0.774 seconds.