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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+80x^68+46x^70+250x^72+20x^73+180x^74+136x^75+448x^76+420x^77+324x^78+1808x^79+559x^80+3800x^81+424x^82+3680x^83+478x^84+1816x^85+342x^86+496x^87+430x^88+84x^89+180x^90+24x^91+184x^92+4x^93+40x^94+76x^96+38x^100+11x^104+4x^108+1x^120

The gray image is a code over GF(2) with n=656, k=14 and d=272.
This code was found by Heurico 1.16 in 11.4 seconds.