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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+50x^63+151x^64+120x^65+119x^66+202x^67+357x^68+596x^69+727x^70+1130x^71+1365x^72+1126x^73+858x^74+530x^75+286x^76+142x^77+53x^78+100x^79+110x^80+42x^81+31x^82+28x^83+29x^84+22x^85+3x^86+8x^87+5x^88+1x^110

The gray image is a code over GF(2) with n=576, k=13 and d=252.
This code was found by Heurico 1.16 in 2.3 seconds.