The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  2  1  4  1  1  1  1 14  1 14  1  1  1  1  4  1 12  1  1  1 10  1  1  1 12 14  1  1  0  2  1  1  0  1  1  6  1  1  1  1  4  1  1  1  1  1  2  1
 0  1  1  6  1  3  5  4  1  2  1  7  9  1  6  1 12 11  3  8  1 14  1  6 15  6  1  1 15  1  2 12 13  1  1 11 13  1  1  0  4  1  1  2 13  0  8 15  1  0 11  5  8  1  3 14 11  7 12  6  2
 0  0  2  0  0  8  8 10  6 10 14 10 14 10  6  4  4 12 14 10  4  2 10  4  8  0  4 10  6  0 12  0  2  0 12  8  8 14 12 14 14 12  2  2  0  2 12  6 12  0  2  4  2 12 10  8 14  4  2  6  2
 0  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  0  0  8  0  0  0  8  0  8  8  8  0  8
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  0  0  0  8  0  0  8  0  8  8  8  8  0  0  8  0  8  8

generates a code of length 61 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+234x^56+520x^57+880x^58+872x^59+1182x^60+1108x^61+1030x^62+892x^63+725x^64+368x^65+192x^66+56x^67+71x^68+12x^69+22x^70+4x^71+8x^72+8x^73+4x^74+2x^76+1x^84

The gray image is a code over GF(2) with n=488, k=13 and d=224.
This code was found by Heurico 1.16 in 0.885 seconds.