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

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

Homogenous weight enumerator: w(x)=1x^0+29x^64+4x^65+89x^66+16x^67+160x^68+96x^69+427x^70+308x^71+887x^72+740x^73+2232x^74+1572x^75+4540x^76+2384x^77+5860x^78+2360x^79+4537x^80+1596x^81+2227x^82+776x^83+889x^84+272x^85+343x^86+84x^87+160x^88+28x^89+50x^90+4x^91+38x^92+22x^94+15x^96+10x^98+5x^100+4x^102+3x^104

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 28.5 seconds.