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

generates a code of length 66 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+30x^57+88x^58+156x^59+162x^60+226x^61+277x^62+404x^63+735x^64+1266x^65+1630x^66+1236x^67+733x^68+420x^69+218x^70+184x^71+122x^72+76x^73+72x^74+56x^75+32x^76+24x^77+17x^78+12x^79+6x^80+4x^81+2x^82+2x^85+1x^100

The gray image is a code over GF(2) with n=528, k=13 and d=228.
This code was found by Heurico 1.16 in 2 seconds.