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  4  4  2  4  2  4  2  1  2  1  4  1  0  8  2  1  8  4  1  0  1  4  2  1
 0 12  0  0  0  0  0  0  0  0  0  8  4  4  4  8 12  0 12 12  4  8  8  8  4  0 12  4 12  4  4  0 12  8 12  8  0  4 12  4  4  4 12  0  4  8  0  0  8  8  4  0  4  4  4  0  4 12  4  0 12 12  8  0 12  8  4
 0  0 12  0  0  0  0  0  0  0  0 12  8 12  4  4 12  4  4  0  8  0 12 12  4  4  0 12  8  0 12  8  8  0  0 12  4  0 12  0  8 12  4  8 12  8  0  4  8  0  0  8 12 12  8  4  4  4  0  4 12  8  4  4  8 12  4
 0  0  0 12  0  0  0  4 12 12  8  4 12  0 12  4  8  0 12 12  8 12  8 12  0  4 12  8  8  8  0  4  0 12  4  8  4  8  4  4  4 12  8  8  8 12  4  0  0  4 12  8  8  8  8 12 12  8 12  0  8  0 12 12  4  4 12
 0  0  0  0 12  0  4  4  4  0  8  0  0  0  0  0  0  8  8 12  4  4  4  4 12 12  8  4  4  8  0  0  8  8  8  4  8  0  8 12  8  4  4  4  4  8  8 12 12  8  0 12 12  0  0  4  0 12  4  8 12 12  4  4  8  0  0
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  0  4  4  4 12  0  8  0  4  8  0  4  8 12 12  4  8 12 12  8  4  8  0  0  8  4  4  0  8  4 12  0 12  8  0  8  4  4 12  8 12  8 12 12  4  4  8  4  4 12  4  8  4
 0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  8  8

generates a code of length 67 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+180x^56+522x^58+40x^59+825x^60+252x^61+1376x^62+1180x^63+2660x^64+2856x^65+4691x^66+3660x^67+4734x^68+2784x^69+2707x^70+1236x^71+1339x^72+248x^73+739x^74+28x^75+400x^76+4x^77+169x^78+96x^80+36x^82+4x^84+1x^100

The gray image is a code over GF(2) with n=536, k=15 and d=224.
This code was found by Heurico 1.16 in 29.6 seconds.