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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+90x^76+10x^77+94x^78+56x^79+167x^80+128x^81+248x^82+184x^83+602x^84+486x^85+1482x^86+1296x^87+2474x^88+1824x^89+2488x^90+1296x^91+1463x^92+486x^93+582x^94+184x^95+218x^96+128x^97+109x^98+56x^99+80x^100+10x^101+65x^102+16x^104+34x^106+5x^108+13x^110+4x^112+1x^114+3x^118+1x^142

The gray image is a code over GF(2) with n=712, k=14 and d=304.
This code was found by Heurico 1.16 in 12.9 seconds.