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  0  2  1  2  8  0  0  1  1  1  2  1  2  1  1  1  2  2  2  1  1  1  1  2  2  1  1  1  1  1  1  2  8  8  8  1  4  1  1  1  1  2  2
 0  2  0  6  0  6  4  2  8 14  6  4 12  4 10  2  0  8  2  2  0  6  8  2 14 10 14  2  2  2  2 12 14  6  0  2  8 14  4  6 10 10  2 10 10  4 10  6  2 12  6 12 12  6 14  2  4  2  4  2 14  8  8  8  4  6
 0  0 12  0  0  0  4  0 12  0  0 12  8  0  8  8  8  8  4  4  4 12  4  0 12  4  0  0  4 12  8  4  4  4  0  8 12  8 12  0  4  0  8 12 12  0 12  4  8  4  4  4  0  4  0  0 12 12  4  4  8  4  0  8  0  0
 0  0  0 12  0  0  0  4  0  8  4  0  0  0 12  8 12 12  0 12 12  8  4 12 12 12  4  8  0 12  8  4  0  0  0  4  8  4 12  0  4  8  8 12  0  8  8 12 12  0  8  4  4  4  0  8  4  4 12  4 12 12 12 12  4  0
 0  0  0  0 12  0  0  8  4 12  4  4  4  8  4  4 12  8  8 12  0  4 12 12 12  4  0 12  4  8 12  8  8 12  0  0  4  8  4  0  0  8  0  0 12 12 12  0  4  0  8  0  8  0 12 12  8  8  0 12  4  4  4 12  8  0
 0  0  0  0  0  8  0  8  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0

generates a code of length 66 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+108x^56+64x^57+364x^58+272x^59+709x^60+1100x^61+1718x^62+2372x^63+3260x^64+4284x^65+4240x^66+4428x^67+3339x^68+2572x^69+1458x^70+956x^71+630x^72+292x^73+262x^74+36x^75+180x^76+8x^77+72x^78+25x^80+14x^82+3x^84+1x^92

The gray image is a code over GF(2) with n=528, k=15 and d=224.
This code was found by Heurico 1.16 in 23.1 seconds.