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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+65x^76+18x^77+86x^78+68x^79+139x^80+156x^81+246x^82+220x^83+835x^84+348x^85+1728x^86+448x^87+1727x^88+320x^89+839x^90+224x^91+218x^92+162x^93+103x^94+60x^95+56x^96+20x^97+37x^98+4x^99+23x^100+21x^102+5x^104+5x^106+3x^108+5x^110+1x^114+1x^134

The gray image is a code over GF(2) with n=696, k=13 and d=304.
This code was found by Heurico 1.16 in 3.5 seconds.