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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+64x^64+28x^66+257x^68+4x^69+196x^70+36x^71+491x^72+144x^73+1084x^74+336x^75+3070x^76+504x^77+4048x^78+504x^79+3019x^80+336x^81+1084x^82+144x^83+476x^84+36x^85+172x^86+4x^87+196x^88+44x^90+58x^92+32x^96+11x^100+4x^104+1x^120

The gray image is a code over GF(2) with n=624, k=14 and d=256.
This code was found by Heurico 1.16 in 10.5 seconds.