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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+218x^76+28x^77+124x^79+344x^80+360x^81+448x^82+1016x^83+683x^84+364x^85+64x^86+140x^87+156x^88+16x^89+97x^92+27x^96+9x^100+1x^140

The gray image is a code over GF(2) with n=664, k=12 and d=304.
This code was found by Heurico 1.16 in 100 seconds.