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

generates a code of length 88 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+44x^80+76x^81+75x^82+126x^83+113x^84+306x^85+317x^86+814x^87+504x^88+790x^89+298x^90+278x^91+60x^92+90x^93+42x^94+18x^95+31x^96+30x^97+27x^98+12x^99+15x^100+12x^101+4x^102+8x^105+4x^106+1x^150

The gray image is a code over GF(2) with n=704, k=12 and d=320.
This code was found by Heurico 1.16 in 1.26 seconds.