The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  4  1  1  1 14  1 10  1  1  1  0  1  1  1  2  1  1 14  1  1  2  1  1  8  1  1  1  1  2  4  1  1  1  1 12  2  1 10  1  4 10  1  0  1 12  8  0  1  1  1  1  1  1  1  1  1 12  0  4  1 12
 0  1  1  6  1  3  5  4  1  2  1  7  1 12  9 15  1 10  1 11 12  6  1 13  5 15  1  4  1  1  8 10  1  1  8  1 15 14 12 15  1  1  3 15  5  2  1  1 10  1  8  1  1  7  1  0 12  1  2  5 10  6 12 15 12  9 11 13  1  1  1  1  1
 0  0  2  0  0  8  8 10  6 10 14  2 10 14  6  8  2 14  0  2  0  4 12  4  4  6  0  4  8 12  0  6  2  2 10 14 12  4  6  4  4  2  6  0 14 12  8 12  4 14  4  4  2  8  0 10  2 14 10 12  8 14  6  4 12 10 14  2  4  6 14 14  8
 0  0  0  8  0  8  0  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  0  0  0  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  8  8  8  8  0  0  8  0  0  8  8  8  8  0  8  8  8  0  8  8
 0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  8  8  0  0  8  8  8  0  0  8  0  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0  0  8  0  8  8  8  0  0  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+358x^68+478x^69+1084x^70+720x^71+1260x^72+776x^73+1148x^74+648x^75+817x^76+380x^77+301x^78+32x^79+107x^80+24x^81+15x^82+8x^83+12x^84+6x^85+10x^86+4x^88+1x^92+1x^94+1x^98

The gray image is a code over GF(2) with n=584, k=13 and d=272.
This code was found by Heurico 1.16 in 1.29 seconds.