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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+200x^62+140x^63+541x^64+440x^65+1007x^66+1116x^67+1771x^68+1860x^69+2315x^70+1920x^71+1824x^72+1152x^73+877x^74+396x^75+382x^76+132x^77+137x^78+12x^79+80x^80+34x^82+32x^84+4x^86+6x^88+2x^90+2x^92+1x^100

The gray image is a code over GF(2) with n=560, k=14 and d=248.
This code was found by Heurico 1.16 in 7.17 seconds.