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  0  1  2  1  0  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  8  1  1  2  1  0  1  1  4  2  1  1  1  1  1  1  2  2  1  1  8  1  2  1  0  0  1  2  1  1  1  1  2
 0  2  0  6  0 14  8 10  4  6 10  4 12  6  4 10  0  6 10 12  4  2  8 14 10  2  0 14 10  2  8  4  6 12  8  6 10 14  4  4 10  2  6  2 12 10  2  8  8  6  2  2  4  6  2  2 14  4  0  2  2  2  0  2  8 14  2  4  2 12  2  2  6  2  2 10 12  8  6
 0  0 12  0  0  8  4  8  4  4  4  8  8 12 12 12  0  0 12 12 12  0 12  4 12  8  8 12  8  8  0  0  8  4  8 12 12 12  0  8  0 12  8  0  4  4  8  0 12  0  8 12  0  0  4  4 12  0 12 12 12  0  4  8 12  8 12  0 12  0  0  4  0  8  4  0  0  8  0
 0  0  0 12  0  8  0  4  4  4 12 12 12  0  4  8 12 12  0  0 12  8 12 12 12  8  8  0  0  4  4  0  4  8  8  4  0  8 12  8  4 12  0 12 12  0 12  4  4  4  4 12 12 12  8  4  0  4  4  4  4  8  4  8  0 12 12  8 12  0  4  8  8  8 12  0  8  8  8
 0  0  0  0 12  4 12  4  4  0 12  8  4 12  8  0 12  4  4 12 12  0  8 12  8  0 12  0  4 12  8  0  0  8  8  0 12  8  8 12 12 12  8 12  8  8  8  0  8 12  0  8  4 12  0 12  0  0  4  0 12  8  8 12  4 12  4 12  4  8  8 12  8  8  8  4  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+233x^72+72x^73+438x^74+344x^75+594x^76+956x^77+872x^78+1368x^79+803x^80+928x^81+564x^82+360x^83+303x^84+60x^85+162x^86+8x^87+68x^88+30x^90+8x^92+12x^94+3x^96+2x^100+2x^102+1x^124

The gray image is a code over GF(2) with n=632, k=13 and d=288.
This code was found by Heurico 1.16 in 13.5 seconds.