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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+27x^70+66x^71+81x^72+104x^73+151x^74+266x^75+441x^76+624x^77+699x^78+618x^79+426x^80+244x^81+108x^82+40x^83+53x^84+28x^85+28x^86+18x^87+16x^88+20x^89+5x^90+14x^91+6x^92+4x^93+5x^94+2x^95+1x^134

The gray image is a code over GF(2) with n=624, k=12 and d=280.
This code was found by Heurico 1.16 in 0.945 seconds.