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

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

Homogenous weight enumerator: w(x)=1x^0+56x^69+166x^70+282x^71+391x^72+550x^73+895x^74+1260x^75+1601x^76+1998x^77+2185x^78+1974x^79+1576x^80+1248x^81+824x^82+516x^83+345x^84+178x^85+125x^86+64x^87+37x^88+24x^89+24x^90+22x^91+14x^92+8x^93+4x^94+8x^95+2x^96+2x^97+2x^99+1x^104+1x^114

The gray image is a code over GF(2) with n=624, k=14 and d=276.
This code was found by Heurico 1.16 in 7.99 seconds.