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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+145x^72+180x^74+36x^75+295x^76+260x^77+736x^78+952x^79+686x^80+248x^81+216x^82+36x^83+121x^84+4x^85+80x^86+49x^88+28x^90+12x^92+8x^94+2x^96+1x^136

The gray image is a code over GF(2) with n=632, k=12 and d=288.
This code was found by Heurico 1.16 in 1.65 seconds.