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  2  1  1  4  1  1  1  1  1  1  1  1  1  1  1  2  1  2  4
 0 12  0  4  0  0  4 12  0  0  4 12  0  4 12  0  8 12  8 12  8 12  0 12  8  0 12 12  8  4  4  0  0 12  8 12  4  8 12  4  0  4  8 12  0  0  0 12  8  4  8  8  4  0 12  0 12  4  8  4  4  8  0  0  8  0  4  8 12 12  4  8  8  0  4  4 12
 0  0 12  4  0 12  4  0 12  0  4  0  0  4  0 12  4  8  0 12  4  8  0  4  4  0  4  8  8 12  0 12  8  4  4  8  8 12 12  0  8 12 12  4  4  0  8  0  8  8 12  0  8  4  0  0 12  8  8 12  4  8  4  4 12  8  4  0  4 12 12 12 12 12  0 12  0
 0  0  0  8  0  0  8  0  0  8  0  8  8  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  0  0  0
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  0  0  8  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  8  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0  0  8  0  8  8  0  8  0  0  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+16x^73+32x^74+112x^75+390x^76+752x^77+288x^78+144x^79+98x^80+58x^84+18x^88+1x^144

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 2.54 seconds.