The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+175x^54+84x^55+546x^56+436x^57+943x^58+1084x^59+1863x^60+1920x^61+2241x^62+2016x^63+1903x^64+1172x^65+935x^66+396x^67+335x^68+56x^69+146x^70+4x^71+64x^72+30x^74+22x^76+10x^78+1x^80+1x^88

The gray image is a code over GF(2) with n=496, k=14 and d=216.
This code was found by Heurico 1.16 in 7.72 seconds.