The generator matrix

 1  0  0  1  1  1  8  1  1 14  1  1 12 14  1  1  2  1 14 12  1 14  1  1 10  1  2  1  1  4  1  0  1  1 10  1  4  1  8  1  1  1  0  2  6  1  1 14 14  1 10 12  1  1  1  8  8  1 12  4  1  6  2 12  1  1  1  1  1  2 12  1
 0  1  0  0  5 13  1 10  3  1  8  1  1  2  9  6  1  7  1  6  2  4  3 15  1 14  1 13 12  1  8  1 15 12 10  6  1  1  2  9  2 10  1  0  1 14  4  1  1  3  1 12 10  0  5  1  1 15  8  1  4  1  1  1  8 10 13  6 10  2  1  8
 0  0  1  3 11  4  5 12  8 12  5 13  7  1 10 13  9  2 10  1  6  1 15 15  7  6  6  7  5  8 14  1 13  6  1 11 14 13  1 12  5  4 11  1  9  2 12  4 15  4  4  1 10  6  1  2  4  1  1  4 15 14  0  9  2  7  0  8  9  1  4  8
 0  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  8  0  8  8  8  0  8  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  8  0  0  0  0  0  8  0  8  8  8  0  0  8  0  8  8  0  0  8  0  0  0

generates a code of length 72 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+697x^68+794x^69+1445x^70+688x^71+1405x^72+760x^73+882x^74+414x^75+402x^76+168x^77+240x^78+54x^79+102x^80+22x^81+8x^82+12x^83+1x^92+1x^94

The gray image is a code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 0.871 seconds.