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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+31x^76+78x^77+94x^78+164x^79+231x^80+286x^81+346x^82+540x^83+663x^84+526x^85+419x^86+246x^87+133x^88+96x^89+66x^90+42x^91+15x^92+44x^93+23x^94+14x^95+13x^96+6x^97+8x^98+2x^99+4x^101+2x^102+2x^106+1x^132

The gray image is a code over GF(2) with n=672, k=12 and d=304.
This code was found by Heurico 1.16 in 0.982 seconds.