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

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

Homogenous weight enumerator: w(x)=1x^0+64x^57+127x^58+174x^59+242x^60+346x^61+507x^62+754x^63+975x^64+1672x^65+2274x^66+2258x^67+2301x^68+1648x^69+957x^70+750x^71+445x^72+256x^73+164x^74+128x^75+101x^76+78x^77+60x^78+32x^79+31x^80+32x^81+6x^82+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 8.04 seconds.