The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^54+116x^55+469x^56+364x^57+925x^58+1216x^59+1995x^60+1860x^61+2303x^62+1968x^63+1854x^64+1140x^65+867x^66+400x^67+319x^68+92x^69+168x^70+12x^71+83x^72+31x^74+13x^76+7x^78+1x^80+1x^82+1x^84

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 7.48 seconds.