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

generates a code of length 88 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+69x^76+56x^77+140x^78+142x^79+236x^80+240x^81+340x^82+422x^83+671x^84+1196x^85+1566x^86+2104x^87+2238x^88+2078x^89+1575x^90+1110x^91+634x^92+400x^93+299x^94+222x^95+169x^96+92x^97+114x^98+82x^99+51x^100+28x^101+46x^102+12x^103+18x^104+6x^105+7x^106+2x^107+7x^108+4x^110+2x^112+4x^114+1x^126

The gray image is a code over GF(2) with n=704, k=14 and d=304.
This code was found by Heurico 1.16 in 12.1 seconds.