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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+24x^72+2x^73+42x^74+114x^75+76x^76+492x^77+75x^78+140x^79+27x^80+18x^81+10x^82+2x^83+1x^142

The gray image is a code over GF(2) with n=616, k=10 and d=288.
This code was found by Heurico 1.16 in 0.41 seconds.