The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4  2  1  1  1  1 10  1  4  1  2  1  1  1  1  8  8  1 10  1  1  1  8  1 14  1  0  1  1  1  1  1  1  1  4  6  1 12  1  1  8  1 10  2  4  1  8  1  1  1  1  4  1  1  2  1  4 12  1 12 10  0  2  4  1  1  1
 0  1  1  0  3  1  5  4  1 12 15  1  1 14 15  5  2  1  7  1  6  1  5  6 12  5  1  1 12  1  9  4 15  1  4  1  7  1 14 15  5  2  0  9  6  1  1 10  1  3  1  1 12  1  0  1  3  1  1  2 13 12  1 13 13  1  6 12  1 13  4  1  4 14  2  8  7  8
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2  4  6  2  6  6  4  4 12 10 12  2 12  6 10  8  4  8  4  6  6  4 14 10 12  4  4  8  6  6  2 14  6  0  0  8  0  2 12  6 10 10  6 10 12 12 12 10 12  8  4 14 10  2 12  0  2  0  2 14  2  8  4  4
 0  0  0  2  0  2  2  8 14  6 14 12 10  4 10  0  4  4 12  2  2  8  2  2  4 12  8  4 12 14 12  2 10 10  0  2 10  4 12  8 14  2 14 10 14 14  6 12  8  8  4 10  6  0  4  4  2  8 10  2  0 10 10  6  6  0  0  8 14  6  0  8 10 14 10  8  0  8
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  0  0  8  8  8  8  8  0  0  8  0  8  0  0  0  8  8  8  8  0  8  0  0  0  8  0  0  0  0  0  8  8  8  0  0  0  8  0  0  0  8  8  0  8  0  0  8  0  0  0  0  8  0  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  8  0  0  0  8  8  0  0  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  0  8

generates a code of length 78 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+76x^69+414x^70+804x^71+1720x^72+2264x^73+4176x^74+4576x^75+6963x^76+6914x^77+9510x^78+6896x^79+7825x^80+4742x^81+3729x^82+2000x^83+1433x^84+656x^85+409x^86+166x^87+125x^88+62x^89+27x^90+20x^91+10x^92+6x^93+3x^94+2x^95+1x^96+4x^98+2x^100

The gray image is a code over GF(2) with n=624, k=16 and d=276.
This code was found by Heurico 1.16 in 60.9 seconds.