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

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

Homogenous weight enumerator: w(x)=1x^0+138x^72+28x^74+160x^75+386x^76+704x^77+280x^78+160x^79+107x^80+12x^82+69x^84+2x^88+1x^148

The gray image is a code over GF(2) with n=616, k=11 and d=288.
This code was found by Heurico 1.16 in 30.8 seconds.