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

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

Homogenous weight enumerator: w(x)=1x^0+79x^76+2x^77+46x^78+22x^79+105x^80+44x^81+89x^82+64x^83+76x^84+122x^85+336x^86+174x^87+833x^88+4272x^89+851x^90+152x^91+328x^92+126x^93+78x^94+90x^95+45x^96+36x^97+51x^98+8x^99+37x^100+6x^101+38x^102+2x^103+21x^104+24x^106+7x^108+12x^110+3x^112+8x^114+1x^116+2x^118+1x^138

The gray image is a code over GF(2) with n=712, k=13 and d=304.
This code was found by Heurico 1.16 in 3.81 seconds.