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  0  2  1  1  8  2  2  8  1  2  1  1  1  2  0  1  8  1  1 12  1  1  2 12  1  1  0  1  1  4  2  2  8  0  1  2  0  1  1  1  1  2  8  1  8  1
 0  2  0  6  0  6  4  2  8 14  6  4 12  4 10  2  0  8  2  2  0  6 10  0  6  8  2  6  0 14  2 14 14  2  4 10  6 12  2  2  2  2  2 12 12  2  8  6 10  2  2  4  2  2  0  2 10 10  2  2 10  6  4 14 14  4 14  4  2 10  4  8
 0  0 12  0  0  0  4  0 12  0  0 12  8  0  8  8  8  8  4  4  4 12 12  4  4  8  4 12  4  4  0 12  0  4  4  8 12  0  0  8  8  4 12 12  0  8 12 12 12  8  4  8 12  8 12  8  4 12  4  4  4  0  0  8  4  4  8  4 12  8 12  0
 0  0  0 12  0  0  0  4  0  8  4  0  0  0 12  8 12 12  0 12 12  8 12 12  4  8  8  0 12  4  0  4  8 12  8  4  8  0 12  8  0  4  0 12  4  8  0  0 12  8  8  4  0  8 12  4 12  4 12  0  4 12  8  0  8  0  8  8  4 12 12  0
 0  0  0  0 12  0  0  8  4 12  4  4  4  8  4  4 12  8  8 12  0  4  0  0  8  4  4  4  4  4  4  4  4 12  0 12  8  8  8 12  8  0  8  8 12  0  4  4  0  0 12  4  4  4 12 12  0  0  8  8 12 12 12 12 12  4 12 12 12  0  4  4
 0  0  0  0  0  8  0  8  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  0  0  8  8  0  0  8  8  8  0  0  8  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0  0  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  0

generates a code of length 72 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+176x^62+28x^63+495x^64+280x^65+986x^66+1016x^67+2061x^68+2192x^69+3252x^70+3480x^71+4471x^72+4016x^73+3648x^74+2048x^75+1731x^76+912x^77+928x^78+332x^79+351x^80+24x^81+178x^82+8x^83+79x^84+44x^86+25x^88+4x^90+1x^92+1x^96

The gray image is a code over GF(2) with n=576, k=15 and d=248.
This code was found by Heurico 1.16 in 26.1 seconds.