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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+126x^70+8x^71+212x^72+100x^73+368x^74+388x^75+680x^76+568x^77+562x^78+352x^79+316x^80+100x^81+126x^82+20x^83+57x^84+52x^86+35x^88+10x^90+8x^92+4x^94+2x^100+1x^124

The gray image is a code over GF(2) with n=616, k=12 and d=280.
This code was found by Heurico 1.16 in 0.985 seconds.