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

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

Homogenous weight enumerator: w(x)=1x^0+130x^62+8x^63+370x^64+56x^65+600x^66+180x^67+883x^68+852x^69+1912x^70+1976x^71+2670x^72+1960x^73+1900x^74+868x^75+748x^76+196x^77+424x^78+40x^79+275x^80+8x^81+174x^82+97x^84+38x^86+11x^88+6x^90+1x^104

The gray image is a code over GF(2) with n=576, k=14 and d=248.
This code was found by Heurico 1.16 in 8.69 seconds.