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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+28x^77+95x^78+132x^79+179x^80+218x^81+281x^82+290x^83+496x^84+756x^85+1166x^86+1616x^87+1941x^88+2108x^89+1913x^90+1654x^91+1161x^92+774x^93+463x^94+284x^95+206x^96+154x^97+114x^98+102x^99+74x^100+40x^101+40x^102+16x^103+27x^104+16x^105+14x^106+2x^107+5x^108+2x^109+4x^110+6x^112+5x^114+1x^122

The gray image is a code over GF(2) with n=712, k=14 and d=308.
This code was found by Heurico 1.16 in 12.6 seconds.