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

generates a code of length 73 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+76x^72+128x^73+32x^74+16x^76+2x^88+1x^112

The gray image is a code over GF(2) with n=584, k=8 and d=288.
This code was found by Heurico 1.16 in 0.322 seconds.