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

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

Homogenous weight enumerator: w(x)=1x^0+188x^68+12x^69+414x^70+44x^71+629x^72+312x^73+1030x^74+968x^75+1820x^76+1648x^77+2316x^78+1904x^79+1745x^80+904x^81+924x^82+280x^83+553x^84+68x^85+272x^86+4x^87+164x^88+106x^90+39x^92+26x^94+12x^96+1x^112

The gray image is a code over GF(2) with n=624, k=14 and d=272.
This code was found by Heurico 1.16 in 9.77 seconds.