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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+78x^65+96x^66+136x^67+184x^68+210x^69+389x^70+646x^71+760x^72+604x^73+401x^74+200x^75+110x^76+86x^77+52x^78+32x^79+21x^80+18x^81+15x^82+16x^83+10x^84+12x^85+5x^86+10x^87+2x^90+1x^92+1x^116

The gray image is a code over GF(2) with n=576, k=12 and d=260.
This code was found by Heurico 1.16 in 1.08 seconds.