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

generates a code of length 73 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+104x^68+256x^70+288x^71+236x^72+480x^73+128x^74+224x^75+104x^76+32x^77+128x^78+66x^80+1x^128

The gray image is a code over GF(2) with n=584, k=11 and d=272.
This code was found by Heurico 1.16 in 0.406 seconds.