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

generates a code of length 67 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+141x^58+202x^59+235x^60+298x^61+401x^62+434x^63+783x^64+1172x^65+2562x^66+3888x^67+2523x^68+1196x^69+919x^70+398x^71+237x^72+246x^73+192x^74+156x^75+98x^76+64x^77+68x^78+40x^79+23x^80+22x^81+4x^82+2x^83+4x^84+2x^85+1x^98

The gray image is a code over GF(2) with n=536, k=14 and d=228.
This code was found by Heurico 1.16 in 8.59 seconds.