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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+64x^68+224x^69+299x^70+628x^71+700x^72+1550x^73+1533x^74+2730x^75+2500x^76+4748x^77+3222x^78+4478x^79+2514x^80+2894x^81+1457x^82+1252x^83+608x^84+610x^85+242x^86+232x^87+90x^88+76x^89+49x^90+18x^91+16x^92+10x^93+13x^94+6x^95+3x^96+1x^106

The gray image is a code over GF(2) with n=624, k=15 and d=272.
This code was found by Heurico 1.16 in 25.3 seconds.