The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  0  1  1 12  1  1  1 10  1  0  1  1  1  6  1 10  1  1 12  0  6  1  1  1 10  1  1 12  1  1  1  1  1  0  1  6  1  1  1  6  1  1  1 10  0  1 12  1  1  0  1 12  1 10 12  2  1  6  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  1  5 12  1 15 10  9  1  0  1  3  5  6  1  9  1 10  5  1  1  1 15 12  3  1  0  6  1  9 15  5 10 12  1  0  1  6 12  5  1  3  5  0  1  1 10  1  0 15  1 10  1 15  1  1 12  0  1  3  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  0  0  8  0  8  0  8  0  8  8  8  0  0  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  8  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  0  8  8  8  0  0  0  8  8  8  8  8  0  0  8  8  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  8  0  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  8  0  8  0  0  8  0  0  8  8  8  0  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  8  8  0  8  0  0  0  8  0  0  0  0  8  8  8  0  0  8  0  0  0  8  8  0  8  8  0  0  8  0  8  8  0  8  8  8  8  0  8  8  8  0  8  0  8  0  0  0  0  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  0  0  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  0  8  0  0  8  8  8  0  0  8  8  0  8  0  8  0  8  8  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  8  8  0  0  0  8  0  0  0  0  8  8  0  0  0  8  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  0  8  8  0  8  0  0  8  0  8  8  0  0  8  0  0  0  8  8  8  0  0  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+56x^64+34x^66+28x^67+281x^68+156x^69+296x^70+684x^71+1026x^72+2272x^73+3238x^74+5484x^75+5574x^76+8792x^77+9744x^78+8792x^79+5615x^80+5472x^81+3262x^82+2260x^83+929x^84+684x^85+296x^86+156x^87+223x^88+32x^89+26x^90+4x^91+81x^92+16x^96+14x^100+7x^104+1x^108

The gray image is a code over GF(2) with n=624, k=16 and d=256.
This code was found by Heurico 1.16 in 64.5 seconds.