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

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

Homogenous weight enumerator: w(x)=1x^0+42x^64+202x^66+4x^67+342x^68+40x^69+620x^70+140x^71+946x^72+608x^73+1533x^74+1944x^75+3790x^76+3424x^77+5520x^78+3400x^79+3858x^80+1936x^81+1625x^82+612x^83+892x^84+120x^85+537x^86+44x^87+255x^88+16x^89+148x^90+91x^92+42x^94+17x^96+11x^98+4x^100+1x^102+1x^104+1x^106+1x^108

The gray image is a code over GF(2) with n=624, k=15 and d=256.
This code was found by Heurico 1.16 in 36.6 seconds.