The generator matrix

 1  0  1  1  1  6  1  1  0  6  1  1  0  1  1  6  1  1  1 10  1  0  1  1  1  1  1  4  1  1 14  1  4  1 14  1  1  2  1  1  1 14  1  8  1 10  1  2  1  4  1  1  6 12  1  0  1  1  1 14  8  1  1  2  1  1  6  1 12  1  8  1
 0  1 11  6  1  1  8 11  1  1 14 13  1 14 11  1  4  1 11  1  8  1  6  5 12  5  3  1 10  4  1 15  1 15  1  5  8  1 14  5  3  1  2  1 15  1  6  1  5  1  5 12  1  1  2  1  3 10  9  1  1  2  5  1  1  4  1  2  2  9  4  8
 0  0 12  0  0  0  0  0  0  8  8  4  4  4  0 12  4 12 12 12 12  4 12  4 12  0  8  0 12  8 12  0 12  4  8  4  0  8  8  0 12  8  8  4  4 12  4  4  4  4  8  0  0  8  0  0 12  0  0  8  0 12  4 12 12  8  0  8 12  4  4  0
 0  0  0 12  0  0 12  8  4 12  8  8  4  8  4  8 12  4 12 12  0  0  4  0  8 12  0  0  4 12  0  0 12  0  4 12  8  0  4  4 12  8 12  4  0  4  8  4  4  8  8  8 12  0  4  8  4 12  8  0  4  8  8 12 12  0  8  0  0  8  0  0
 0  0  0  0  4  0  8  4  4 12  4  0  8  0  0 12  4 12  4  8  0 12  8 12  4 12  8 12  0  4  8  8  4 12  0  8  4  4 12 12  8  8  0 12  4  8  4  4  4  0 12  8  0  8  0 12  0 12  0 12  0 12  8  8  0 12 12  0  0 12  8 12
 0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  8  0  0  8  0  8  0  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  0  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+46x^63+170x^64+292x^65+626x^66+924x^67+1851x^68+2702x^69+3476x^70+4200x^71+4253x^72+4442x^73+3390x^74+2518x^75+1883x^76+942x^77+512x^78+188x^79+129x^80+78x^81+43x^82+22x^83+26x^84+20x^85+11x^86+6x^87+6x^88+4x^89+5x^90+1x^94+1x^96

The gray image is a code over GF(2) with n=576, k=15 and d=252.
This code was found by Heurico 1.16 in 16.4 seconds.