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

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

Homogenous weight enumerator: w(x)=1x^0+56x^63+109x^64+110x^65+180x^66+242x^67+222x^68+410x^69+802x^70+1286x^71+1530x^72+1260x^73+768x^74+372x^75+220x^76+140x^77+130x^78+120x^79+69x^80+42x^81+34x^82+34x^83+22x^84+18x^85+4x^86+2x^87+2x^88+4x^89+2x^90+1x^112

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 2.5 seconds.