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  1  1  1  1  1  1  1  1  1  1  1  4  1  1  1  1  1  1  1  1  1  8  1  1  1  1  1
 0 12  0 12  0 12  0  4  8 12  0 12  0 12  8  4  0  4 12  0  8 12  4  8 12  4  0  8 12  4  0  8  8  0 12 12  4  0  0  8 12  4 12  4  8  0  8  4  4  0  4  0  8  0  0 12  8 12  0  8  4 12
 0  0  8  0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  0  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  0
 0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  8  8  0  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  0  0  0  8  8  0  8  0  0  0  8  0  8  8  8  8  0  0  8  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  0  0  8  8  8  0  8  8  0  8  0  0  8  8  8  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  8  8  0  0  0  0  8  0  8  0  8
 0  0  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  0  8  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0  0  0  8  0  0  8  0  8  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  8  8  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0

generates a code of length 62 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+55x^56+48x^58+208x^60+512x^61+560x^62+512x^63+31x^64+16x^66+48x^68+16x^70+40x^72+1x^120

The gray image is a code over GF(2) with n=496, k=11 and d=224.
This code was found by Heurico 1.16 in 0.283 seconds.